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Theory Of Stochastic Processes
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Book Synopsis The Theory of Stochastic Processes I by : Iosif I. Gikhman
Download or read book The Theory of Stochastic Processes I written by Iosif I. Gikhman and published by Springer. This book was released on 2015-03-30 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Reviews: "Gihman and Skorohod have done an excellent job of presenting the theory in its present state of rich imperfection." --D.W. Stroock, Bulletin of the American Mathematical Society, 1980
Book Synopsis Stochastic Processes: General Theory by : Malempati M. Rao
Download or read book Stochastic Processes: General Theory written by Malempati M. Rao and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory and Applications of Stochastic Processes by : Zeev Schuss
Download or read book Theory and Applications of Stochastic Processes written by Zeev Schuss and published by Springer Science & Business Media. This book was released on 2009-12-09 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical. This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.
Book Synopsis Stochastic Processes and Filtering Theory by : Andrew H. Jazwinski
Download or read book Stochastic Processes and Filtering Theory written by Andrew H. Jazwinski and published by Courier Corporation. This book was released on 2013-04-15 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well. Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probability theory and stochastic processes, the author introduces and defines the problems of filtering, prediction, and smoothing. He presents the mathematical solutions to nonlinear filtering problems, and he specializes the nonlinear theory to linear problems. The final chapters deal with applications, addressing the development of approximate nonlinear filters, and presenting a critical analysis of their performance.
Book Synopsis Probability Theory and Stochastic Processes by : Pierre Brémaud
Download or read book Probability Theory and Stochastic Processes written by Pierre Brémaud and published by Springer Nature. This book was released on 2020-04-07 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory of Stochastic Objects by : Athanasios Christou Micheas
Download or read book Theory of Stochastic Objects written by Athanasios Christou Micheas and published by CRC Press. This book was released on 2018-01-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book defines and investigates the concept of a random object. To accomplish this task in a natural way, it brings together three major areas; statistical inference, measure-theoretic probability theory and stochastic processes. This point of view has not been explored by existing textbooks; one would need material on real analysis, measure and probability theory, as well as stochastic processes - in addition to at least one text on statistics- to capture the detail and depth of material that has gone into this volume. Presents and illustrates ‘random objects’ in different contexts, under a unified framework, starting with rudimentary results on random variables and random sequences, all the way up to stochastic partial differential equations. Reviews rudimentary probability and introduces statistical inference, from basic to advanced, thus making the transition from basic statistical modeling and estimation to advanced topics more natural and concrete. Compact and comprehensive presentation of the material that will be useful to a reader from the mathematics and statistical sciences, at any stage of their career, either as a graduate student, an instructor, or an academician conducting research and requiring quick references and examples to classic topics. Includes 378 exercises, with the solutions manual available on the book's website. 121 illustrative examples of the concepts presented in the text (many including multiple items in a single example). The book is targeted towards students at the master’s and Ph.D. levels, as well as, academicians in the mathematics, statistics and related disciplines. Basic knowledge of calculus and matrix algebra is required. Prior knowledge of probability or measure theory is welcomed but not necessary.
Book Synopsis Stochastic Processes by : Pierre Del Moral
Download or read book Stochastic Processes written by Pierre Del Moral and published by CRC Press. This book was released on 2017-02-24 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Processes by : Robert G. Gallager
Download or read book Stochastic Processes written by Robert G. Gallager and published by Cambridge University Press. This book was released on 2013-12-12 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive textbook on stochastic processes, written by one of the world's leading information theorists, covering both theory and applications.
Book Synopsis Limit Theorems for Stochastic Processes by : Jean Jacod
Download or read book Limit Theorems for Stochastic Processes written by Jean Jacod and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A First Look At Stochastic Processes by : Jeffrey S Rosenthal
Download or read book A First Look At Stochastic Processes written by Jeffrey S Rosenthal and published by World Scientific. This book was released on 2019-09-26 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory.Interspersed throughout are applications to such topics as gambler's ruin probabilities, random walks on graphs, sequence waiting times, branching processes, stock option pricing, and Markov Chain Monte Carlo (MCMC) algorithms.The focus is always on making the theory as well-motivated and accessible as possible, to allow students and readers to learn this fascinating subject as easily and painlessly as possible.
Book Synopsis Introduction to the Theory of Random Processes by : Iosif Il?ich Gikhman
Download or read book Introduction to the Theory of Random Processes written by Iosif Il?ich Gikhman and published by Courier Corporation. This book was released on 1996-01-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rigorous exposition suitable for elementary instruction. Covers measure theory, axiomatization of probability theory, processes with independent increments, Markov processes and limit theorems for random processes, more. A wealth of results, ideas, and techniques distinguish this text. Introduction. Bibliography. 1969 edition.
Book Synopsis The Theory of Stochastic Processes by : D.R. Cox
Download or read book The Theory of Stochastic Processes written by D.R. Cox and published by Routledge. This book was released on 2017-09-04 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book should be of interest to undergraduate and postgraduate students of probability theory.
Book Synopsis Lectures on the Theory of Stochastic Processes by : Anatolij V. Skorochod
Download or read book Lectures on the Theory of Stochastic Processes written by Anatolij V. Skorochod and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-01-14 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Lectures on the Theory of Stochastic Processes".
Book Synopsis Introduction To Stochastic Processes by : Mu-fa Chen
Download or read book Introduction To Stochastic Processes written by Mu-fa Chen and published by World Scientific. This book was released on 2021-05-25 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this book is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts — Markov chains and stochastic analysis. The readers are led directly to the core of the main topics to be treated in the context. Further details and additional materials are left to a section containing abundant exercises for further reading and studying.In the part on Markov chains, the focus is on the ergodicity. By using the minimal nonnegative solution method, we deal with the recurrence and various types of ergodicity. This is done step by step, from finite state spaces to denumerable state spaces, and from discrete time to continuous time. The methods of proofs adopt modern techniques, such as coupling and duality methods. Some very new results are included, such as the estimate of the spectral gap. The structure and proofs in the first part are rather different from other existing textbooks on Markov chains.In the part on stochastic analysis, we cover the martingale theory and Brownian motions, the stochastic integral and stochastic differential equations with emphasis on one dimension, and the multidimensional stochastic integral and stochastic equation based on semimartingales. We introduce three important topics here: the Feynman-Kac formula, random time transform and Girsanov transform. As an essential application of the probability theory in classical mathematics, we also deal with the famous Brunn-Minkowski inequality in convex geometry.This book also features modern probability theory that is used in different fields, such as MCMC, or even deterministic areas: convex geometry and number theory. It provides a new and direct routine for students going through the classical Markov chains to the modern stochastic analysis.
Book Synopsis Stochastic Processes by : Toshio Nakagawa
Download or read book Stochastic Processes written by Toshio Nakagawa and published by Springer Science & Business Media. This book was released on 2011-05-27 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reliability theory is of fundamental importance for engineers and managers involved in the manufacture of high-quality products and the design of reliable systems. In order to make sense of the theory, however, and to apply it to real systems, an understanding of the basic stochastic processes is indispensable. As well as providing readers with useful reliability studies and applications, Stochastic Processes also gives a basic treatment of such stochastic processes as: the Poisson process, the renewal process, the Markov chain, the Markov process, and the Markov renewal process. Many examples are cited from reliability models to show the reader how to apply stochastic processes. Furthermore, Stochastic Processes gives a simple introduction to other stochastic processes such as the cumulative process, the Wiener process, the Brownian motion and reliability applications. Stochastic Processes is suitable for use as a reliability textbook by advanced undergraduate and graduate students. It is also of interest to researchers, engineers and managers who study or practise reliability and maintenance.
Book Synopsis Adventures in Stochastic Processes by : Sidney I. Resnick
Download or read book Adventures in Stochastic Processes written by Sidney I. Resnick and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Stochastic Processes with R by : Robert P. Dobrow
Download or read book Introduction to Stochastic Processes with R written by Robert P. Dobrow and published by John Wiley & Sons. This book was released on 2016-03-07 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to stochastic processes through the use of R Introduction to Stochastic Processes with R is an accessible and well-balanced presentation of the theory of stochastic processes, with an emphasis on real-world applications of probability theory in the natural and social sciences. The use of simulation, by means of the popular statistical software R, makes theoretical results come alive with practical, hands-on demonstrations. Written by a highly-qualified expert in the field, the author presents numerous examples from a wide array of disciplines, which are used to illustrate concepts and highlight computational and theoretical results. Developing readers’ problem-solving skills and mathematical maturity, Introduction to Stochastic Processes with R features: More than 200 examples and 600 end-of-chapter exercises A tutorial for getting started with R, and appendices that contain review material in probability and matrix algebra Discussions of many timely and stimulating topics including Markov chain Monte Carlo, random walk on graphs, card shuffling, Black–Scholes options pricing, applications in biology and genetics, cryptography, martingales, and stochastic calculus Introductions to mathematics as needed in order to suit readers at many mathematical levels A companion web site that includes relevant data files as well as all R code and scripts used throughout the book Introduction to Stochastic Processes with R is an ideal textbook for an introductory course in stochastic processes. The book is aimed at undergraduate and beginning graduate-level students in the science, technology, engineering, and mathematics disciplines. The book is also an excellent reference for applied mathematicians and statisticians who are interested in a review of the topic.
