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The purpose of this monograph is to provide a theory of Markov processes that are invariant under the actions of Lie groups, focusing on ways to represent such processes in the spirit of the classical Lévy-Khinchin representation. It interweaves probability theory, topology, and global analysis on manifolds to present the most recent results in a developing area of stochastic analysis. The author’s discussion is structured with three different levels of generality:— A Markov process in a Lie group G that is invariant under the left (or right) translations— A Markov process xt in a manifold X that is invariant under the transitive action of a Lie group G on X— A Markov process xt invariant under the non-transitive action of a Lie group GA large portion of the text is devoted to the representation of inhomogeneous Lévy processes in Lie groups and homogeneous spaces by a time dependent triple through a martingale property. Preliminary definitions and results in both stochastics and Lie groups are provided in a series of appendices, making the book accessible to those who may be non-specialists in either of these areas. Invariant Markov Processes Under Lie Group Actions will be of interest to researchers in stochastic analysis and probability theory, and will also appeal to experts in Lie groups, differential geometry, and related topics interested in applications of their own subjects.
Book Synopsis Invariant Markov Processes Under Lie Group Actions by : Ming Liao
Download or read book Invariant Markov Processes Under Lie Group Actions written by Ming Liao and published by Springer. This book was released on 2018-06-28 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this monograph is to provide a theory of Markov processes that are invariant under the actions of Lie groups, focusing on ways to represent such processes in the spirit of the classical Lévy-Khinchin representation. It interweaves probability theory, topology, and global analysis on manifolds to present the most recent results in a developing area of stochastic analysis. The author’s discussion is structured with three different levels of generality:— A Markov process in a Lie group G that is invariant under the left (or right) translations— A Markov process xt in a manifold X that is invariant under the transitive action of a Lie group G on X— A Markov process xt invariant under the non-transitive action of a Lie group GA large portion of the text is devoted to the representation of inhomogeneous Lévy processes in Lie groups and homogeneous spaces by a time dependent triple through a martingale property. Preliminary definitions and results in both stochastics and Lie groups are provided in a series of appendices, making the book accessible to those who may be non-specialists in either of these areas. Invariant Markov Processes Under Lie Group Actions will be of interest to researchers in stochastic analysis and probability theory, and will also appeal to experts in Lie groups, differential geometry, and related topics interested in applications of their own subjects.
Eugene B. Dynkin published his first paper, on Markov chain theory, whilst still an undergraduate student at Moscow State University. He went on to make fundamental contributions to the theory of Markov processes and to Lie groups, generating entire schools in these areas.
Book Synopsis The Dynkin Festschrift by : Mark Iosifovich Freĭdlin
Download or read book The Dynkin Festschrift written by Mark Iosifovich Freĭdlin and published by Springer Science & Business Media. This book was released on 1994 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eugene B. Dynkin published his first paper, on Markov chain theory, whilst still an undergraduate student at Moscow State University. He went on to make fundamental contributions to the theory of Markov processes and to Lie groups, generating entire schools in these areas.
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
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
Book Synopsis An Introduction to Finite Markov Processes by : S. R. Adke
Download or read book An Introduction to Finite Markov Processes written by S. R. Adke and published by John Wiley & Sons. This book was released on 1984 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Invariant Measures for Markov Processes by : Yūji Itō
Download or read book Invariant Measures for Markov Processes written by Yūji Itō and published by . This book was released on 1962 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Invariant Distributions for Monotone Markov Processes by : Hugo A. Hopenhayn
Download or read book Invariant Distributions for Monotone Markov Processes written by Hugo A. Hopenhayn and published by . This book was released on 1987 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Symmetric Markov Processes by : M.L. Silverstein
Download or read book Symmetric Markov Processes written by M.L. Silverstein and published by Lecture Notes in Mathematics. This book was released on 1974-12-16 with total page 308 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.
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.
The top Lyapunov exponent of a system of stochastic differential equations was investigated. Brownian motion paths on a Riemannian manifold were discussed and several theoretical results were obtained. A new asymptotic formula for the volume of a small extrinsic ball in a submanifold was obtained. Finally, an invariance principle for Lie groups was obtained.
Book Synopsis Markov Processes Applied to Control, Replacement, and Signal Analysis by : Mark A. Pinsky
Download or read book Markov Processes Applied to Control, Replacement, and Signal Analysis written by Mark A. Pinsky and published by . This book was released on 1987 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: The top Lyapunov exponent of a system of stochastic differential equations was investigated. Brownian motion paths on a Riemannian manifold were discussed and several theoretical results were obtained. A new asymptotic formula for the volume of a small extrinsic ball in a submanifold was obtained. Finally, an invariance principle for Lie groups was obtained.
Book Synopsis On Certain Extensions of a Rotation Invariant Markov Process by : Juha Vuolle-Apiala
Download or read book On Certain Extensions of a Rotation Invariant Markov Process written by Juha Vuolle-Apiala and published by . This book was released on 2000 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
