Stochastic Processes General Theory

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Stochastic Processes: General Theory

Malempati M. Rao
Stochastic Processes General Theory Book PDF

Author : Malempati M. Rao
Publisher : Springer Science & Business Media
Page : 629 pages
File Size : 41,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475765984

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Stochastic Processes: General Theory by Malempati M. Rao Pdf

Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and includes an extended account of martingales and their generalizations. Various compositions of (quasi- or semi-)martingales and their integrals are given. Here the Bochner boundedness principle plays a unifying role: a unique feature of the book. Applications to higher order stochastic differential equations and their special features are presented in detail. Stochastic processes in a manifold and multiparameter stochastic analysis are also discussed. Each of the seven chapters includes complements, exercises and extensive references: many avenues of research are suggested. The book is a completely revised and enlarged version of the author's Stochastic Processes and Integration (Noordhoff, 1979). The new title reflects the content and generality of the extensive amount of new material. Audience: Suitable as a text/reference for second year graduate classes and seminars. A knowledge of real analysis, including Lebesgue integration, is a prerequisite.

Statistics of Random Processes II

Robert Shevilevich Lipt︠s︡er,Alʹbert Nikolaevich Shiri︠a︡ev
Statistics of Random Processes II Book PDF

Author : Robert Shevilevich Lipt︠s︡er,Alʹbert Nikolaevich Shiri︠a︡ev
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 45,7 Mb
Release : 2001
Category : Mathematics
ISBN : 3540639284

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Statistics of Random Processes II by Robert Shevilevich Lipt︠s︡er,Alʹbert Nikolaevich Shiri︠a︡ev Pdf

"Written by two renowned experts in the field, the books under review contain a thorough and insightful treatment of the fundamental underpinnings of various aspects of stochastic processes as well as a wide range of applications. Providing clear exposition, deep mathematical results, and superb technical representation, they are masterpieces of the subject of stochastic analysis and nonlinear filtering....These books...will become classics." --SIAM REVIEW

Stochastic Processes

Pierre Del Moral,Spiridon Penev
Stochastic Processes Book PDF

Author : Pierre Del Moral,Spiridon Penev
Publisher : CRC Press
Page : 866 pages
File Size : 50,5 Mb
Release : 2017-02-24
Category : Mathematics
ISBN : 9781498701846

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Stochastic Processes by Pierre Del Moral,Spiridon Penev Pdf

Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.

An Introduction to the Theory of Point Processes

D.J. Daley,D. Vere-Jones
An Introduction to the Theory of Point Processes Book PDF

Author : D.J. Daley,D. Vere-Jones
Publisher : Springer Science & Business Media
Page : 471 pages
File Size : 47,8 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9780387215648

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An Introduction to the Theory of Point Processes by D.J. Daley,D. Vere-Jones Pdf

Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.

Probability Theory and Stochastic Processes

Pierre Brémaud
Probability Theory and Stochastic Processes Book PDF

Author : Pierre Brémaud
Publisher : Springer Nature
Page : 713 pages
File Size : 41,6 Mb
Release : 2020-04-07
Category : Mathematics
ISBN : 9783030401832

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Probability Theory and Stochastic Processes by Pierre Brémaud Pdf

The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, physics, computer and communications networks, and signal processing. In order to help the reader to reach a level of technical autonomy sufficient to understand the presented models, this book includes a reasonable dose of probability theory. On the other hand, the study of stochastic processes gives an opportunity to apply the main theoretical results of probability theory beyond classroom examples and in a non-trivial manner that makes this discipline look more attractive to the applications-oriented student. One can distinguish three parts of this book. The first four chapters are about probability theory, Chapters 5 to 8 concern random sequences, or discrete-time stochastic processes, and the rest of the book focuses on stochastic processes and point processes. There is sufficient modularity for the instructor or the self-teaching reader to design a course or a study program adapted to her/his specific needs. This book is in a large measure self-contained.

Limit Theorems for Stochastic Processes

Jean Jacod,Albert N. Shiryaev
Limit Theorems for Stochastic Processes Book PDF

Author : Jean Jacod,Albert N. Shiryaev
Publisher : Springer Science & Business Media
Page : 620 pages
File Size : 45,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662025147

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Limit Theorems for Stochastic Processes by Jean Jacod,Albert N. Shiryaev Pdf

Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an elementary introduction to the main topics: theory of martingales and stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students.

The Theory of Stochastic Processes III

I. I. Gihman,A. V. Skorohod
The Theory of Stochastic Processes III Book PDF

Author : I. I. Gihman,A. V. Skorohod
Publisher : Springer Science & Business Media
Page : 393 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461580652

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The Theory of Stochastic Processes III by I. I. Gihman,A. V. Skorohod Pdf

It was originally planned that the Theory of Stochastic Processes would consist of two volumes: the first to be devoted to general problems and the second to specific cJasses of random processes. It became apparent, however, that the amount of material related to specific problems of the theory could not possibly be incJuded in one volume. This is how the present third volume came into being. This voJume contains the theory of martingales, stochastic integrals, stochastic differential equations, diffusion, and continuous Markov processes. The theory of stochastic processes is an actively developing branch of mathe matics, and it would be an unreasonable and impossible task to attempt to encompass it in a single treatise (even a multivolume one). Therefore, the authors, guided by their own considerations concerning the relative importance of various results, naturally had to be selective in their choice of material. The authors are fully aware that such a selective process is not perfecL Even a number of topics that are, in the authors' opinion, of great importance could not be incJuded, for example, limit theorems for particular cJasses of random processes, the theory of random fields, conditional Markov processes, and information and statistics of random processes. With the publication of this last volume, we recall with gratitude oUf associates who assisted us in this endeavor, and express our sincere thanks to G.N. Sytaya, L.V. Lobanova, P.V. Boiko, N.F. Ryabova, N.A. Skorohod, V.V. Skorohod, N.I. Portenko, and L.I. Gab.

Statistics of Random Processes I

R.S. Liptser,A.N. Shiryaev
Statistics of Random Processes I Book PDF

Author : R.S. Liptser,A.N. Shiryaev
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 54,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475716658

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Statistics of Random Processes I by R.S. Liptser,A.N. Shiryaev Pdf

A considerable number of problems in the statistics of random processes are formulated within the following scheme. On a certain probability space (Q, ff, P) a partially observable random process (lJ,~) = (lJ ~/), t :;::-: 0, is given with only the second component n ~ = (~/), t:;::-: 0, observed. At any time t it is required, based on ~h = g., ° s sst}, to estimate the unobservable state lJ/. This problem of estimating (in other words, the filtering problem) 0/ from ~h will be discussed in this book. It is well known that if M(lJ;)

Stochastic Processes and Applications

Grigorios A. Pavliotis
Stochastic Processes and Applications Book PDF

Author : Grigorios A. Pavliotis
Publisher : Springer
Page : 345 pages
File Size : 43,7 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9781493913237

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Stochastic Processes and Applications by Grigorios A. Pavliotis Pdf

This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

Adventures in Stochastic Processes

Sidney I. Resnick
Adventures in Stochastic Processes Book PDF

Author : Sidney I. Resnick
Publisher : Springer Science & Business Media
Page : 640 pages
File Size : 52,8 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781461203872

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Adventures in Stochastic Processes by Sidney I. Resnick Pdf

Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. This text offers easy access to this fundamental topic for many students of applied sciences at many levels. It includes examples, exercises, applications, and computational procedures. It is uniquely useful for beginners and non-beginners in the field. No knowledge of measure theory is presumed.

Discrete Stochastic Processes

Robert G. Gallager
Discrete Stochastic Processes Book PDF

Author : Robert G. Gallager
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461523291

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Discrete Stochastic Processes by Robert G. Gallager Pdf

Stochastic processes are found in probabilistic systems that evolve with time. Discrete stochastic processes change by only integer time steps (for some time scale), or are characterized by discrete occurrences at arbitrary times. Discrete Stochastic Processes helps the reader develop the understanding and intuition necessary to apply stochastic process theory in engineering, science and operations research. The book approaches the subject via many simple examples which build insight into the structure of stochastic processes and the general effect of these phenomena in real systems. The book presents mathematical ideas without recourse to measure theory, using only minimal mathematical analysis. In the proofs and explanations, clarity is favored over formal rigor, and simplicity over generality. Numerous examples are given to show how results fail to hold when all the conditions are not satisfied. Audience: An excellent textbook for a graduate level course in engineering and operations research. Also an invaluable reference for all those requiring a deeper understanding of the subject.

Controlled Stochastic Processes

I. I. Gihman,A. V. Skorohod
Controlled Stochastic Processes Book PDF

Author : I. I. Gihman,A. V. Skorohod
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461262022

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Controlled Stochastic Processes by I. I. Gihman,A. V. Skorohod Pdf

The theory of controlled processes is one of the most recent mathematical theories to show very important applications in modern engineering, parti cularly for constructing automatic control systems, as well as for problems of economic control. However, actual systems subject to control do not admit a strictly deterministic analysis in view of random factors of various kinds which influence their behavior. Such factors include, for example, random noise occurring in the electrical system, variations in the supply and demand of commodities, fluctuations in the labor force in economics, and random failures of components on an automated line. The theory of con trolled processes takes the random nature of the behavior of a system into account. In such cases it is natural, when choosing a control strategy, to proceed from the average expected result, taking note of all the possible variants of the behavior of a controlled system. An extensive literature is devoted to various economic and engineering systems of control (some of these works are listed in the Bibliography). is no text which adequately covers the general However, as of now there mathematical theory of controlled processes. The authors ofthis monograph have attempted to fill this gap. In this volume the general theory of discrete-parameter (time) controlled processes (Chapter 1) and those with continuous-time (Chapter 2), as well as the theory of controlled stochastic differential equations (Chapter 3), are presented.

Probability Theory and Stochastic Processes with Applications (Second Edition)

Oliver Knill
Probability Theory and Stochastic Processes with Applications Second Edition Book PDF

Author : Oliver Knill
Publisher : World Scientific Publishing Company
Page : 500 pages
File Size : 41,7 Mb
Release : 2017-01-31
Category : Mathematics
ISBN : 9813109491

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Probability Theory and Stochastic Processes with Applications (Second Edition) by Oliver Knill Pdf

This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.

An Introduction to Stochastic Processes and Their Applications

Petar Todorovic
An Introduction to Stochastic Processes and Their Applications Book PDF

Author : Petar Todorovic
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461397427

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An Introduction to Stochastic Processes and Their Applications by Petar Todorovic Pdf

This text on stochastic processes and their applications is based on a set of lectures given during the past several years at the University of California, Santa Barbara (UCSB). It is an introductory graduate course designed for classroom purposes. Its objective is to provide graduate students of statistics with an overview of some basic methods and techniques in the theory of stochastic processes. The only prerequisites are some rudiments of measure and integration theory and an intermediate course in probability theory. There are more than 50 examples and applications and 243 problems and complements which appear at the end of each chapter. The book consists of 10 chapters. Basic concepts and definitions are pro vided in Chapter 1. This chapter also contains a number of motivating ex amples and applications illustrating the practical use of the concepts. The last five sections are devoted to topics such as separability, continuity, and measurability of random processes, which are discussed in some detail. The concept of a simple point process on R+ is introduced in Chapter 2. Using the coupling inequality and Le Cam's lemma, it is shown that if its counting function is stochastically continuous and has independent increments, the point process is Poisson. When the counting function is Markovian, the sequence of arrival times is also a Markov process. Some related topics such as independent thinning and marked point processes are also discussed. In the final section, an application of these results to flood modeling is presented.

Model Theory of Stochastic Processes

Sergio Fajardo,H. Jerome Keisler
Model Theory of Stochastic Processes Book PDF

Author : Sergio Fajardo,H. Jerome Keisler
Publisher : Cambridge University Press
Page : 136 pages
File Size : 49,5 Mb
Release : 2017-03-30
Category : Mathematics
ISBN : 9781108619264

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Model Theory of Stochastic Processes by Sergio Fajardo,H. Jerome Keisler Pdf

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the fourteenth publication in the Lecture Notes in Logic series, Fajardo and Keisler present new research combining probability theory and mathematical logic. It is a general study of stochastic processes using ideas from model theory, a key central theme being the question, 'When are two stochastic processes alike?' The authors assume some background in nonstandard analysis, but prior knowledge of model theory and advanced logic is not necessary. This volume will appeal to mathematicians willing to explore new developments with an open mind.