Markov Set-Chains

	Author(s):	Darald J. Hartfiel
	Collection:	Lecture Notes in Mathematics 1695
	Publisher:	Springer-Verlag Berlin Heidelberg
	Year:	1998
	Language:	English
	Pages:	134 pages
	Size:	712 KB
	Extension:	DJVU

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[content title="Description"]In this study extending classical Markov chain theory to handle fluctuating transition matrices, the author develops a theory of Markov set-chains and provides numerous examples showing how that theory can be applied. Chapters are concluded with a discussion of related research. Readers who can benefit from this monograph are those interested in, or involved with, systems whose data is imprecise or that fluctuate with time. A background equivalent to a course in linear algebra and one in probability theory should be sufficient.

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[content title="Content"] [/content]

[content title="About the author"]Darald J. Hartfiel is a mathematician [/content]

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Finite Markov Chains and Algorithmic Applications

	Author(s):	Olle Häggström
	Collection:	London Mathematical Society student texts 52
	Publisher:	Cambridge University Press
	Year:	2002
	Language:	English
	Pages:	123 pages
	Size:	573 KB
	Extension:	PDF

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[content title="Description"]This text is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before using it to study a range of randomized algorithms with important applications in optimization and other problems in computing. The book will appeal not only to mathematicians, but to students of computer science who will discover much useful material. This clear and concise introduction to the subject has numerous exercises that will help students to deepen their understanding.
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[content title="About the author"]Olle Häggström (born 4 October 1967) is a professor of mathematical statistics at Chalmers University of Technology. Häggström earned his doctorate in 1994 at Chalmers University of Technology with Jeffrey Steif as supervisor.
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Continuous Strong Markov Processes in Dimension One : A stochastic calculus approach

	Author(s):	Sigurd Assing, Wolfgang M. Schmidt
	Collection:	Lecture Notes in Mathematics 1688
	Publisher:	Springer-Verlag Berlin Heidelberg
	Year:	1998
	Language:	English
	Pages:	145 pages
	Size:	822 KB
	Extension:	DJVU

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[content title="Description"]The book presents an in-depth study of arbitrary one-dimensional continuous strong Markov processes using methods of stochastic calculus. Departing from the classical approaches, a unified investigation of regular as well as arbitrary non-regular diffusions is provided. A general construction method for such processes, based on a generalization of the concept of a perfect additive functional, is developed. The intrinsic decomposition of a continuous strong Markov semimartingale is discovered. The book also investigates relations to stochastic differential equations and fundamental examples of irregular diffusions. [/content]

[content title="Content"] [/content]

[content title="About the author"]Dr Sigurd Assing works mostly in probability theory, with particular interest in: random processes, stochastic analysis, statistical mechanics and stochastic control.Wolfgang M. Schmidt (born 3 October 1933, Vienna, Austria) is a mathematician working in the area of number theory. He studied mathematics at the University of Vienna, where he received his PhD, which was supervised by Edmund Hlawka, in 1955. Wolfgang Schmidt is a Professor Emeritus from the University of Colorado at Boulder and a member of the Austrian Academy of Sciences and the Polish Academy of Sciences.



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Markov Decision Processes with Their Applications

	Author(s):	Qiying Hu, Wuyi Yue
	Collection:	Advances in Mechanics and Mathematics 14
	Publisher:	Springer US
	Year:	2008
	Language:	English
	Pages:	305 pages
	Size:	1.74 MB
	Extension:	PDF

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[content title="Description"]Markov decision processes (MDPs), also called stochastic dynamic programming, were first studied in the 1960s. MDPs can be used to model and solve dynamic decision-making problems that are multi-period and occur in stochastic circumstances. There are three basic branches in MDPs: discrete-time MDPs, continuous-time MDPs and semi-Markov decision processes. Starting from these three branches, many generalized MDPs models have been applied to various practical problems. These models include partially observable MDPs, adaptive MDPs, MDPs in stochastic environments, and MDPs with multiple objectives, constraints or imprecise parameters.

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[content title="About the author"]Qi-Ying Hu
VP:Formulations, Omega Therapeutics Inc.Wuyi Yue received the B. Eng. degree in Electronic Engineering from Tsinghua University, China and the M. Eng. and Dr. Eng. degrees in Applied Mathematics and Physics from Kyoto University, Japan. She was a Researcher and a Chief Researcher of ASTEM RI, an Associate Professor of Wakayama University, an Associate Professor and a Professor at the Department of Applied Mathematics, a Professor at Department of Information Science and Systems Engineering, Konan University, Japan. [/content]

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Stochastic integration and differential equations

	Author(s):	Philip E. Protter
	Collection:	Applications of mathematics 21 0172-4568
	Publisher:	Springer
	Year:	2004
	Language:	English
	Pages:	430 pages
	Size:	3.16 MB
	Extension:	DJVU

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[content title="Description"]It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emery's examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.
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[content title="About the author"]Philip E. Protter is Ph.D. University of California, San Diego 1975[/content]

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Diffusion, Markov processes and martingales. Ito calculus - Volume 2

	Author(s):	L. C. G. Rogers, David Williams
	Collection:	Cambridge Mathematical Library
	Publisher:	Cambridge University Press
	Year:	2000
	Language:	English
	Pages:	469 pages
	Size:	3.13 MB
	Extension:	DJVU

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[content title="Description"]The second volume concentrates on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. These subjects are made accessible in the many concrete examples that illustrate techniques of calculation, and in the treatment of all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appear for the first time in this book.
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[content title="Content"] [/content]

[content title="About the author"] David Williams is a mathematician. [/content]

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Markov processes, Gaussian processes and local times

	Author(s):	Michael B. Marcus, Jay Rosen
	Collection:	Cambridge Studies in Advanced Mathematics
	Publisher:	Cambridge University Press
	Year:	2006
	Language:	English
	Pages:	629 pages
	Size:	2.58 MB
	Extension:	PDF

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[content title="Description"]Written by two foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and for experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including sample path properties. It then proceeds to more advanced results, bringing the reader to the heart of contemporary research. It presents the remarkable isomorphism theorems of Dynkin and Eisenbaum, then shows how they can be applied to obtain new properties of Markov processes by using well-established techniques in Gaussian process theory. This original, readable book will appeal to both researchers and advanced graduate students.
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[content title="Content"] [/content]

[content title="About the author"]Michael B. Marcus is a mathematician . [/content]

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An Introduction to Markov Processes

	Author(s):	Daniel W. Stroock
	Collection:	Graduate Texts in Mathematics 230
	Publisher:	Springer-Verlag Berlin Heidelberg
	Year:	2014
	Language:	English
	Pages:	203 pages
	Size:	1.14 MB
	Extension:	DJVU

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[content title="Description"]This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including students from engineering, economics, physics, and biology. Topics covered are: Doeblin's theory, general ergodic properties, and continuous time processes. Applications are dispersed throughout the book. In addition, a whole chapter is devoted to reversible processes and the use of their associated Dirichlet forms to estimate the rate of convergence to equilibrium. These results are then applied to the analysis of the Metropolis (a.k.a simulated annealing) algorithm.

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[content title="About the author"]Daniel Wyler Stroock (born March 20, 1940) is an American mathematician, a probabilist. He is regarded and revered as one of the fundamental contributors to Malliavin calculus with Shigeo Kusuoka and the theory of diffusion processes with S. R. Srinivasa Varadhan with an orientation towards the refinement and further development of Itô’s stochastic calculus. [/content]

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Markov processes, Brownian motion, and time symmetry

	Author(s):	Kai Lai Chung, John B. Walsh
	Collection:	Grundlehren der mathematischen Wissenschaften 249
	Publisher:	Springer
	Year:	2005
	Language:	English
	Pages:	443 pages
	Size:	2.53 MB
	Extension:	DJVU

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[content title="Description"]From the reviews of the First Edition:"This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zurich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites and technicalities. The reader who becomes acquainted with the volume cannot but agree with the reviewer that the author was very successful in accomplishing this goal...The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation. (Mathematical Reviews)This new edition contains 9 new chapters which include new exercises, references, and multiple corrections throughout the original text.
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[content title="About the author"]Chung was a native of Hangzhou, the capital city of Zhejiang Province. Chung entered Tsinghua University in 1936, and initially studied physics at its Department of Physics. In 1940, Chung graduated from the Department of Mathematics of the National Southwestern Associated University, where he later worked as a teaching assistant.[citation needed] During this period, he first studied number theory with Lo-Keng Hua and then probability theory with Pao-Lu Hsu. [/content]

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Markov chains : models, algorithms and applications

	Author(s):	Ching W.-K., Ng M.K.
	Collection:	International series in operations research and management science 83
	Publisher:	Springer
	Year:	2006
	Language:	English
	Pages:	211 pages
	Size:	1.41 MB
	Extension:	PDF

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[content title="Description"]Markov chains are a particularly powerful and widely used tool for analyzing a variety of stochastic (probabilistic) systems over time. This monograph will present a series of Markov models, starting from the basic models and then building up to higher-order models. Included in the higher-order discussions are multivariate models, higher-order multivariate models, and higher-order hidden models. In each case, the focus is on the important kinds of applications that can be made with the class of models being considered in the current chapter. Special attention is given to numerical algorithms that can efficiently solve the models. Therefore, Markov Chains: Models, Algorithms and Applications outlines recent developments of Markov chain models for modeling queueing sequences, Internet, re-manufacturing systems, reverse logistics, inventory systems, bio-informatics, DNA sequences, genetic networks, data mining, and many other practical systems.
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[content title="About the author"]Ching W. Tang (Chinese: 鄧青雲) is a Hong Kong-born American physical chemist. He was born in Yuen Long, Hong Kong in 1947. Tang currently is the Doris Johns Cherry Professor in the Chemical Engineering Department, University of Rochester. He also has joint appointments in the Department of Chemistry and the Department of Physics and Astronomy. Tang has joined HKUST Jockey Club Institute for Advanced Study of the Hong Kong University of Science and Technology as the IAS Bank of East Asia Professor since September 2013.

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Processus de Markov

	Author(s):	Meyer P.-A.
	Collection:	Lecture Notes in Mathematics 0026
	Publisher:	Springer
	Year:	1967
	Language:	English
	Pages:	195 pages
	Size:	1.19 MB
	Extension:	DJVU

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[content title="Description"]In mathematics , a Markov process is a stochastic process possessing the Markov property . In such a process, the prediction of the future from the present is not made more accurate by information about the past. Markov processes are named after their inventor, Andrei Markov .

A discrete-time Markov process is a sequence{\displaystyle \scriptstyle \X_{1},}\scriptstyle\X_{1}, {\displaystyle \scriptstyle \X_{2},}\scriptstyle\X_{2}, {\displaystyle \scriptstyle \X_{3},\\dots }\scriptstyle\X_{3},\\dotsof random variables . The set of their possible values ​​is called the state space , the value{\displaystyle \scriptstyle \ X_{n}\ }\scriptstyle\X_{n}\being the state of the process at the moment{\displaystyle \scriptstyle \ n.}\scriptstyle\n.According to the authors, the term “ Markov chain ” designates discrete-time Markov processes or only discrete-time and discrete-state-space Markov processes, ie. discrete-time Markov processes whose state space is finite or countable . [/content]

[content title="Content"] [/content]

[content title="About the author"]Paul-André Meyer (1934-2003) is a French mathematician .

Elected Correspondent of the Academy of Sciences onMarch 20, 1978, Mathematics section 1 .

Mathematician, former student of the École Normale Supérieure , research director at the CNRS , Paul-André Meyer pursued a career as a researcher at the Louis Pasteur University in Strasbourg . He devoted his scientific work to the theory of potential and the calculus of probabilities , and distinguished himself by his renowned Strasbourg seminar. [/content]

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Chaines de Markov et processus de Poisson

	Author(s):	Lacroix J.
	Collection:
	Publisher:	Univ Curie
	Year:	2002
	Language:	English
	Pages:	107 pages
	Size:	712 KB
	Extension:	DJVU

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[content title="Description"]Chaines de Markov et processus de Poisson [/content]

[content title="Content"] [/content]

[content title="About the author"]Lacroix J. is a mathematician. [/content]

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Generalized hypergeometric functions with applications in statistics and physical sciences

	Author(s):	A. M. Mathai, R. K. Saxena
	Collection:	Lecture Notes in Mathematics 0348
	Publisher:	Springer
	Year:	1973
	Language:	English
	Pages:	321 pages
	Size:	1.57 MB
	Extension:	DJVU

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[content title="Description"]Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences [/content]

[content title="Content"] [/content]

[content title="About the author"]Arakaparampil Mathai "Arak" Mathai (born 28 April 1935) is an Indian mathematician who has worked in Statistics, Applied Analysis, Applications of special functions and Astrophysics. Mathai established the Centre for Mathematical Sciences, Palai, Kerala, India. [/content]

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Information theory and statistics : a tutorial

	Author(s):	Imre Csisz´ar, Paul Shields
	Collection:	Foundations and Trends in Communications and Information Theory
	Publisher:	Now Publishers Inc
	Year:	2004
	Language:	English
	Pages:	122 pages
	Size:	1.03 MB
	Extension:	PDF

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[content title="Description"]Information Theory and Statistics: A Tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting. The topics covered include large deviations, hypothesis testing, maximum likelihood estimation in exponential families, analysis of contingency tables, and iterative algorithms with an "information geometry" background. Also, an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory. The tutorial does not assume the reader has an in-depth knowledge of Information Theory or statistics. As such, Information Theory and Statistics: A Tutorial, is an excellent introductory text to this highly-important topic in mathematics, computer science and electrical engineering. It provides both students and researchers with an invaluable resource to quickly get up to speed in the field.
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[content title="About the author"]
Paul Shields is an American mathematician.Imre Csiszár (Hungarian: [ˈimrɛ ˈt͡ʃisaːr]) is a Hungarian mathematician with contributions to information theory and probability theory. In 1996 he won the Claude E. Shannon Award, the highest annual award given in the field of information theory.

He was born on February 7, 1938, in Miskolc, Hungary. He became interested in mathematics in middle school. He was inspired by his father who was a forest engineer and was among the first to use mathematical techniques in his area. He studied mathematics at the Eötvös Loránd University, Budapest, and received his Diploma in 1961. He got his PhD in 1967 and the scientific degree Doctor of Mathematical Science in 1977. [/content]

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Lectures on Probability Theory and Statistics : Ecole d’Eté de Probabilités

	Author(s):	Evarist Giné, Geoffrey R. Grimmett, Laurent Saloff-Coste, Pierre Bernard
	Collection:	Lecture Notes in Mathematics 1665
	Publisher:	Springer-Verlag Berlin Heidelberg
	Year:	1997
	Language:	English
	Pages:	430 pages
	Size:	2.74 MB
	Extension:	DJVU

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[content title="Description"]Lecture Notes in Mathematics 1665, reports on new developments in mathematical research and teaching-quickly, informally and at a high level. Paper.
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[content title="Content"] [/content]

[content title="About the author"]Evarist Giné, Mathematics Department Head, Dies
Giné was a distinguished mathematician who worked on mathematical statistics and probability in infinite dimensions.Saloff-Coste obtained his doctorate in 1983 at the Pierre-et-Marie-Curie University , where he completed his postgraduate thesis. The second part of his doctorate ( Doctorat d'état ), was obtained in 1989, under the supervision of Nicolas Varopoulos with a thesis entitled Harmonic analysis and real analysis on groups 1 . In the 1990s, he was a professor at the Université Toulouse-III-Paul-Sabatier and, since the early 2000s, he was a professor of mathematics at Cornell University in Ithaca, New York , where he also chairs the Faculty (2012). [/content]

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Nonparametric Statistics for Stochastic Processes Estimation and Prediction

	Author(s):	D. Bosq
	Collection:	Lecture Notes in Statistics 110
	Publisher:	Springer-Verlag New York
	Year:	1998
	Language:	English
	Pages:	232 pages
	Size:	1.19 MB
	Extension:	DJVU

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[content title="Description"]This book is devoted to the theory and applications of nonparametic functional estimation and prediction. Chapter 1 provides an overview of inequalities and limit theorems for strong mixing processes. Density and regression estimation in discrete time are studied in Chapter 2 and 3. The special rates of convergence which appear in continuous time are presented in Chapters 4 and 5. This second edition is extensively revised and it contains two new chapters. Chapter 6 discusses the surprising local time density estimator. Chapter 7 gives a detailed account of implementation of nonparametric method and practical examples in economics, finance and physics. Comarison with ARMA and ARCH methods shows the efficiency of nonparametric forecasting. The prerequisite is a knowledge of classical probability theory and statistics. Denis Bosq is Professor of Statistics at the Unviersity of Paris 6 (Pierre et Marie Curie). He is Editor-in-Chief of "Statistical Inference for Stochastic Processes" and an editor of "Journal of Nonparametric Statistics". He is an elected member of the International Statistical Institute. He has published about 90 papers or works in nonparametric statistics and four books.
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[content title="About the author"]D. Bosq has PhD University of Paris 1971[/content]

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Group Representations in Probability and Statistics-Institute of Mathematical Statistics

	Author(s):	Persi Diaconis
	Collection:	Lecture Notes Vol 11
	Publisher:	Institute of Mathematical Statistics
	Year:	1988
	Language:	English
	Pages:	204 pages
	Size:	3.27 MB
	Extension:	DJVU

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[content title="Description"]This monograph is an expanded version of lecture notes I have used over the past eight years.. I first taught this subject at Harvard's Department of Statistics 1981-82 when a version of these notes were issued. I've subsequently taught the subject at Stanford in 1983 and 1986. I've also delivered lecture series on this material at Ohio State and at St.. Flour.. This means that I've had the benefit of dozens of critics and proofreaders the graduate students and faculty who sat in. Jim Fill, Arunas Rudvalis and Hansmartin Zeuner were particularly helpful. Four students went on to write theses in the subject - Douglas Critchlow, Peter Matthews, Andy Greenhalgh and Dan Rockmore. Their ideas have certainly enriched the present version.
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[content title="About the author"]Persi Diaconis , born onJanuary 31 , 1945in New York , is an American mathematician who was formerly a professional magician. He is a professor of mathematics and statistics at Stanford University . He is particularly known for his work on random problems, such as card shuffling.

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Bayesian Spectrum Analysis and Parameter Estimation

	Author(s):	G. Larry Bretthorst
	Collection:	Lecture Notes in Statistics 48
	Publisher:	Springer-Verlag New York
	Year:	1988
	Language:	English
	Pages:	220 pages
	Size:	1.31 MB
	Extension:	PDF

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[content title="Description"]This book is primarily a research document on the application of probability theory to the parameter estimation problem. The people who will be interested in this material are physicists, chemists, economists, and engineers who have to deal with data on a daily basis; consequently, we have included a great deal of introductory and tutorial material. Any person with the equivalent of the mathematics background required for the graduate-level study of physics should be able to follow the material contained in this book, though not without effort. In this work we apply probability theory to the problem of estimating parameters in rather general models. In particular when the model consists of a single stationary sinusoid we show that the direct application of probability theory will yield frequency estimates an order of magnitude better than a discrete Fourier transform in signal-to-noise of one. Latter, we generalize the problem and show that probability theory can separate two close frequencies long after the peaks in a discrete Fourier transform have merged.
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[content title="Content"] [/content]

[content title="About the author"]G. Larry Bretthorst is a mathematician [/content]

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Approximation of integrals over asymptotic sets with applications to statistics and probability

	Author(s):	Barbe P.
	Collection:	math PR_0312132
	Publisher:
	Year:	2003
	Language:	English
	Pages:	325 pages
	Size:	2.16 MB
	Extension:	PDF

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[content title="Description"]This book is the first of a larger project that I may try to complete. A second volume should be devoted to the asymptotic analysis of multivariate integrals over small wedges and their applications. A third one should extend some of the results of the first two volumes to the infinite dimensional setting, where there are some potentially amazing applications in the study of stochastic processes.
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[content title="Content"] [/content]

[content title="About the author"]Barbe P. is a mathematician. [/content]

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Lectures on Probability Theory and Statistics : Ecole d’Eté de Probabilités de Saint-Flour XXXI - 2001

	Author(s):	Simon Tavaré, Ofer Zeitouni, Jean Picard
	Collection:	Lecture Notes in Mathematics 1837
	Publisher:	Springer-Verlag Berlin Heidelberg
	Year:	2004
	Language:	English
	Pages:	322 pages
	Size:	2.12 MB
	Extension:	PDF

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[content title="Description"]This volume contains lectures given at the 31st Probability Summer School in Saint-Flour (July 8-25, 2001). Simon Tavaré’s lectures serve as an introduction to the coalescent, and to inference for ancestral processes in population genetics. The stochastic computation methods described include rejection methods, importance sampling, Markov chain Monte Carlo, and approximate Bayesian methods. Ofer Zeitouni’s course on "Random Walks in Random Environment" presents systematically the tools that have been introduced to study the model. A fairly complete description of available results in dimension 1 is given. For higher dimension, the basic techniques and a discussion of some of the available results are provided. The contribution also includes an updated annotated bibliography and suggestions for further reading. Olivier Catoni's course appears separately.

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[content title="About the author"]Simon Tavaré obtained his PhD in Probability and Statistics in 1979 from the University of Sheffield, and began his research career in the USA. After a postdoc with Sam Karlin in Stanford, he held positions in Mathematics at the University of Utah, Statistics at Colorado State University, and Mathematics at the University of Southern California. He held the Kawamoto Chair in Biological Sciences at USC from 1998 to 2014. His research there included work in computational statistics, bioinformatics, probabilistic combinatorics and inference for stochastic processes. Zeitouni received his bachelor's degree in electrical engineering in 1980 from the Technion. He obtained in 1986 his doctorate in electrical engineering under the supervision of Moshe Zakai with the thesis Bounds on the Conditional Density and Maximum a posteriori Estimators for the Nonlinear Filtering Problem.[1] As a postdoc he was a visiting assistant professor at Brown University and at the Laboratory for Information and Decision Systems at MIT. He joined the Technion in 1989 as senior lecturer, and was promoted in 1991 to associate professor, and in 1997 to full professor in the department of electrical engineering. He is now a professor of Mathematics at the Weizmann Institute and at the Courant Institute, and was from 2002 to 2013 a part-time professor at the University of Minnesota.[/content]

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