Markov Processes And Related Problems Of Analysis

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Markov Processes and Related Problems of Analysis

Author : Evgeniĭ Borisovich Dynkin
Publisher : Cambridge University Press
ISBN 13 : 0521285127
Total Pages : 325 pages
Book Rating : 4.5/5 (212 download)

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Book Synopsis Markov Processes and Related Problems of Analysis by : Evgeniĭ Borisovich Dynkin

Download or read book Markov Processes and Related Problems of Analysis written by Evgeniĭ Borisovich Dynkin and published by Cambridge University Press. This book was released on 1982-09-23 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Markov Processes has become a powerful tool in partial differential equations and potential theory with important applications to physics. Professor Dynkin has made many profound contributions to the subject and in this volume are collected several of his most important expository and survey articles. The content of these articles has not been covered in any monograph as yet. This account is accessible to graduate students in mathematics and operations research and will be welcomed by all those interested in stochastic processes and their applications.

Markov Processes and Related Problems of Analysis

Author : Evgeniĭ Borisovich Dynkin
Publisher :
ISBN 13 : 9781107361119
Total Pages : 321 pages
Book Rating : 4.3/5 (611 download)

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Book Synopsis Markov Processes and Related Problems of Analysis by : Evgeniĭ Borisovich Dynkin

Download or read book Markov Processes and Related Problems of Analysis written by Evgeniĭ Borisovich Dynkin and published by . This book was released on 2014-05-14 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Markov Processes has become a powerful tool in partial differential equations and potential theory with important applications to physics. Professor Dynkin has made many profound contributions to the subject and in this volume are collected several of his most important expository and survey articles. The content of these articles has not been covered in any monograph as yet. This account is accessible to graduate students in mathematics and operations research and will be welcomed by all those interested in stochastic processes and their applications.

Markov Processes and Related Problems of Analysis

Author : E. B. Dynkin
Publisher :
ISBN 13 : 9780608175195
Total Pages : 320 pages
Book Rating : 4.1/5 (751 download)

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Book Synopsis Markov Processes and Related Problems of Analysis by : E. B. Dynkin

Download or read book Markov Processes and Related Problems of Analysis written by E. B. Dynkin and published by . This book was released on with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Markov Processes has become a powerful tool in partial differential equations and potential theory with important applications to physics.

Markov Processes and Differential Equations

Author : Mark I. Freidlin
Publisher : Birkhäuser
ISBN 13 : 3034891911
Total Pages : 155 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Markov Processes and Differential Equations by : Mark I. Freidlin

Download or read book Markov Processes and Differential Equations written by Mark I. Freidlin and published by Birkhäuser. This book was released on 2012-12-06 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic methods can be applied very successfully to a number of asymptotic problems for second-order linear and non-linear partial differential equations. Due to the close connection between the second order differential operators with a non-negative characteristic form on the one hand and Markov processes on the other, many problems in PDE's can be reformulated as problems for corresponding stochastic processes and vice versa. In the present book four classes of problems are considered: - the Dirichlet problem with a small parameter in higher derivatives for differential equations and systems - the averaging principle for stochastic processes and PDE's - homogenization in PDE's and in stochastic processes - wave front propagation for semilinear differential equations and systems. From the probabilistic point of view, the first two topics concern random perturbations of dynamical systems. The third topic, homog- enization, is a natural problem for stochastic processes as well as for PDE's. Wave fronts in semilinear PDE's are interesting examples of pattern formation in reaction-diffusion equations. The text presents new results in probability theory and their applica- tion to the above problems. Various examples help the reader to understand the effects. Prerequisites are knowledge in probability theory and in partial differential equations.

Markov Processes, Structure and Asymptotic Behavior

Author : Murray Rosenblatt
Publisher : Springer Science & Business Media
ISBN 13 : 3642652387
Total Pages : 282 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Markov Processes, Structure and Asymptotic Behavior by : Murray Rosenblatt

Download or read book Markov Processes, Structure and Asymptotic Behavior written by Murray Rosenblatt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with a set of related problems in probability theory that are considered in the context of Markov processes. Some of these are natural to consider, especially for Markov processes. Other problems have a broader range of validity but are convenient to pose for Markov processes. The book can be used as the basis for an interesting course on Markov processes or stationary processes. For the most part these questions are considered for discrete parameter processes, although they are also of obvious interest for continuous time parameter processes. This allows one to avoid the delicate measure theoretic questions that might arise in the continuous parameter case. There is an attempt to motivate the material in terms of applications. Many of the topics concern general questions of structure and representation of processes that have not previously been presented in book form. A set of notes comment on the many problems that are still left open and related material in the literature. It is also hoped that the book will be useful as a reference to the reader who would like an introduction to these topics as well as to the reader interested in extending and completing results of this type.

Semi-Markov Processes and Reliability

Author : N. Limnios
Publisher : Springer Science & Business Media
ISBN 13 : 1461201616
Total Pages : 226 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Semi-Markov Processes and Reliability by : N. Limnios

Download or read book Semi-Markov Processes and Reliability written by N. Limnios and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia bility.

Markov Processes

Author : E. B. Dynkin
Publisher : Springer Science & Business Media
ISBN 13 : 3662000318
Total Pages : 377 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Markov Processes by : E. B. Dynkin

Download or read book Markov Processes written by E. B. Dynkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modem theory of Markov processes has its origins in the studies of A. A. MARKOV (1906-1907) on sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian motion (L. BACHELlER 1900, A. EIN STEIN 1905). The first correct mathematical construction of a Markov process with continuous trajectories was given by N. WIENER in 1923. (This process is often called the Wiener process.) The general theory of Markov processes was developed in the 1930's and 1940's by A. N. KOL MOGOROV, W. FELLER, W. DOEBLlN, P. LEVY, J. L. DOOB, and others. During the past ten years the theory of Markov processes has entered a new period of intensive development. The methods of the theory of semigroups of linear operators made possible further progress in the classification of Markov processes by their infinitesimal characteristics. The broad classes of Markov processes with continuous trajectories be came the main object of study. The connections between Markov pro cesses and classical analysis were further developed. It has become possible not only to apply the results and methods of analysis to the problems of probability theory, but also to investigate analytic problems using probabilistic methods. Remarkable new connections between Markov processes and potential theory were revealed. The foundations of the theory were reviewed critically: the new concept of strong Markov process acquired for the whole theory of Markov processes great importance.

Boundary Value Problems and Markov Processes

Author : Kazuaki Taira
Publisher : Springer Science & Business Media
ISBN 13 : 3642016766
Total Pages : 196 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Boundary Value Problems and Markov Processes by : Kazuaki Taira

Download or read book Boundary Value Problems and Markov Processes written by Kazuaki Taira and published by Springer Science & Business Media. This book was released on 2009-06-30 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel’ boundary conditions in probability theory. It presents new developments in the theory of singular integrals.

Diffusion Processes and Related Problems in Analysis, Volume II

Author : V. Wihstutz
Publisher : Springer Science & Business Media
ISBN 13 : 1461203899
Total Pages : 344 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Diffusion Processes and Related Problems in Analysis, Volume II by : V. Wihstutz

Download or read book Diffusion Processes and Related Problems in Analysis, Volume II written by V. Wihstutz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the weekend of March 16-18, 1990 the University of North Carolina at Charlotte hosted a conference on the subject of stochastic flows, as part of a Special Activity Month in the Department of Mathematics. This conference was supported jointly by a National Science Foundation grant and by the University of North Carolina at Charlotte. Originally conceived as a regional conference for researchers in the Southeastern United States, the conference eventually drew participation from both coasts of the U. S. and from abroad. This broad-based par ticipation reflects a growing interest in the viewpoint of stochastic flows, particularly in probability theory and more generally in mathematics as a whole. While the theory of deterministic flows can be considered classical, the stochastic counterpart has only been developed in the past decade, through the efforts of Harris, Kunita, Elworthy, Baxendale and others. Much of this work was done in close connection with the theory of diffusion processes, where dynamical systems implicitly enter probability theory by means of stochastic differential equations. In this regard, the Charlotte conference served as a natural outgrowth of the Conference on Diffusion Processes, held at Northwestern University, Evanston Illinois in October 1989, the proceedings of which has now been published as Volume I of the current series. Due to this natural flow of ideas, and with the assistance and support of the Editorial Board, it was decided to organize the present two-volume effort.

Markov processes and potential theory

Author :
Publisher : Academic Press
ISBN 13 : 9780080873411
Total Pages : 312 pages
Book Rating : 4.8/5 (734 download)

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Book Synopsis Markov processes and potential theory by :

Download or read book Markov processes and potential theory written by and published by Academic Press. This book was released on 2011-08-29 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov Processes and Potential Theory

Theory of Markov Processes

Author : E. B. Dynkin
Publisher : Courier Corporation
ISBN 13 : 0486154866
Total Pages : 226 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Theory of Markov Processes by : E. B. Dynkin

Download or read book Theory of Markov Processes written by E. B. Dynkin and published by Courier Corporation. This book was released on 2012-01-27 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVAn investigation of the logical foundations of the theory behind Markov random processes, this text explores subprocesses, transition functions, and conditions for boundedness and continuity. 1961 edition. /div

Boundary Value Problems and Markov Processes

Author : Kazuaki Taira
Publisher : Springer Nature
ISBN 13 : 3030487881
Total Pages : 502 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Boundary Value Problems and Markov Processes by : Kazuaki Taira

Download or read book Boundary Value Problems and Markov Processes written by Kazuaki Taira and published by Springer Nature. This book was released on 2020-07-01 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 3rd edition provides an insight into the mathematical crossroads formed by functional analysis (the macroscopic approach), partial differential equations (the mesoscopic approach) and probability (the microscopic approach) via the mathematics needed for the hard parts of Markov processes. It brings these three fields of analysis together, providing a comprehensive study of Markov processes from a broad perspective. The material is carefully and effectively explained, resulting in a surprisingly readable account of the subject. The main focus is on a powerful method for future research in elliptic boundary value problems and Markov processes via semigroups, the Boutet de Monvel calculus. A broad spectrum of readers will easily appreciate the stochastic intuition that this edition conveys. In fact, the book will provide a solid foundation for both researchers and graduate students in pure and applied mathematics interested in functional analysis, partial differential equations, Markov processes and the theory of pseudo-differential operators, a modern version of the classical potential theory.

Markov Processes, Semigroups, and Generators

Author : Vassili N. Kolokoltsov
Publisher : Walter de Gruyter
ISBN 13 : 3110250101
Total Pages : 449 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Markov Processes, Semigroups, and Generators by : Vassili N. Kolokoltsov

Download or read book Markov Processes, Semigroups, and Generators written by Vassili N. Kolokoltsov and published by Walter de Gruyter. This book was released on 2011 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work offers a highly useful, well developed reference on Markov processes, the universal model for random processes and evolutions. The wide range of applications, in exact sciences as well as in other areas like social studies, require a volume that offers a refresher on fundamentals before conveying the Markov processes and examples for

Topics in Stochastic Processes

Author : Robert B. Ash
Publisher :
ISBN 13 :
Total Pages : 338 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Topics in Stochastic Processes by : Robert B. Ash

Download or read book Topics in Stochastic Processes written by Robert B. Ash and published by . This book was released on 1975 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Processes, Introduction, Covariance functions, Second order calculus, Karhunen-loeve expansion, Estimation problems, Notes; Spectral theory and prediction, Introduction, L Stochastic integrals, Decomposition of stationary processes, Examples of discrete parameter processes, Discrete parameter prediction: Special cases, Discrete parameter prediction: General solution, Examples of continuous parameter processes; Continuos parameter prediction special cases; yaglom's method, Some stochastic differential equations, Continuos parameter prediction: remarks on the general solution, Notes; Ergodic theory, Ergodicity and mixing, The pointwise ergodic theorem, Applications to real analysis, Applications to Markov chains, The Shannon-mcMillan theorem, Notes; Sample function analysis of continuous parameter stochastic processes, Separability, Measurability, One-Dimensional brownian motion, Law of the iterated logarithm, Markov processes, Processes with independent increments, Continuous parameter martingales, The strong Markov property, Notes; The ito integral and stochastic differential equations, Definitions of the ito integral, Existence and uniqueness theorems for stochastic differential equations, Stochastic differentials: A chain rule, Notes.

Poisson Point Processes and Their Application to Markov Processes

Author : Kiyosi Itô
Publisher : Springer
ISBN 13 : 981100272X
Total Pages : 43 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Poisson Point Processes and Their Application to Markov Processes by : Kiyosi Itô

Download or read book Poisson Point Processes and Their Application to Markov Processes written by Kiyosi Itô and published by Springer. This book was released on 2015-12-24 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ∈ S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S \ {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a one-to-one correspondence between a recurrent extension and a pair of a positive measure k(db) on S \ {a} (called the jumping-in measure and a non-negative number m

Markov Processes

Author : E. B. Dynkin
Publisher : Springer
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Markov Processes by : E. B. Dynkin

Download or read book Markov Processes written by E. B. Dynkin and published by Springer. This book was released on 1969 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applied Semi-Markov Processes

Author : Jacques Janssen
Publisher : Springer Science & Business Media
ISBN 13 : 0387295488
Total Pages : 315 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Applied Semi-Markov Processes by : Jacques Janssen

Download or read book Applied Semi-Markov Processes written by Jacques Janssen and published by Springer Science & Business Media. This book was released on 2006-02-08 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to give to the reader the tools necessary to apply semi-Markov processes in real-life problems. The book is self-contained and, starting from a low level of probability concepts, gradually brings the reader to a deep knowledge of semi-Markov processes. Presents homogeneous and non-homogeneous semi-Markov processes, as well as Markov and semi-Markov rewards processes. The concepts are fundamental for many applications, but they are not as thoroughly presented in other books on the subject as they are here.