Invariant Markov Processes Under Lie Group Actions

Author : Ming Liao
Publisher : Springer
Page : 363 pages
File Size : 42,9 Mb
Release : 2018-06-28
Category : Mathematics
ISBN : 9783319923246

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Invariant Markov Processes Under Lie Group Actions by Ming Liao Pdf

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.

Author : Stefania Ugolini,Marco Fuhrman,Elisa Mastrogiacomo,Paola Morando,Barbara Rüdiger
Publisher : Springer Nature
Page : 273 pages
File Size : 40,8 Mb
Release : 2022-02-09
Category : Mathematics
ISBN : 9783030874322

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Geometry and Invariance in Stochastic Dynamics by Stefania Ugolini,Marco Fuhrman,Elisa Mastrogiacomo,Paola Morando,Barbara Rüdiger Pdf

This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.

Author : Ming Liao
Publisher : Cambridge University Press
Page : 292 pages
File Size : 42,6 Mb
Release : 2004-05-10
Category : Mathematics
ISBN : 0521836530

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Lévy Processes in Lie Groups by Ming Liao Pdf

Up-to-the minute research on important stochastic processes.

Author : Olav Kallenberg
Publisher : Springer Nature
Page : 946 pages
File Size : 48,6 Mb
Release : 2021-02-07
Category : Mathematics
ISBN : 9783030618711

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Foundations of Modern Probability by Olav Kallenberg Pdf

The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.

Author : Mark Pollicott,Klaus Schmidt
Publisher : Cambridge University Press
Page : 496 pages
File Size : 46,7 Mb
Release : 1996-03-28
Category : Mathematics
ISBN : 9780521576888

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Ergodic Theory and Zd Actions by Mark Pollicott,Klaus Schmidt Pdf

A mixture of surveys and original articles that span the theory of Zd actions.

Author : Mark Iosifovich Freĭdlin
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 47,6 Mb
Release : 1994
Category : Mathematics
ISBN : 081763696X

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The Dynkin Festschrift by Mark Iosifovich Freĭdlin Pdf

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.

Author : Robert J. Zimmer
Publisher : University of Chicago Press
Page : 724 pages
File Size : 53,5 Mb
Release : 2019-12-23
Category : Mathematics
ISBN : 9780226568270

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Group Actions in Ergodic Theory, Geometry, and Topology by Robert J. Zimmer Pdf

Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.

Author : L.A. Bunimovich,S.G. Dani,R.L. Dobrushin,M.V. Jakobson,I.P. Kornfeld,N.B. Maslova,Ya.B. Pesin,J. Smillie,Yu.M. Sukhov,A.M. Vershik
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 52,9 Mb
Release : 2000-04-05
Category : Mathematics
ISBN : 3540663169

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Dynamical Systems, Ergodic Theory and Applications by L.A. Bunimovich,S.G. Dani,R.L. Dobrushin,M.V. Jakobson,I.P. Kornfeld,N.B. Maslova,Ya.B. Pesin,J. Smillie,Yu.M. Sukhov,A.M. Vershik Pdf

This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.

Author : Isabelle Chalendar,Jonathan R. Partington
Publisher : Cambridge University Press
Page : 298 pages
File Size : 52,8 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 9781139503297

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Modern Approaches to the Invariant-Subspace Problem by Isabelle Chalendar,Jonathan R. Partington Pdf

One of the major unsolved problems in operator theory is the fifty-year-old invariant subspace problem, which asks whether every bounded linear operator on a Hilbert space has a nontrivial closed invariant subspace. This book presents some of the major results in the area, including many that were derived within the past few years and cannot be found in other books. Beginning with a preliminary chapter containing the necessary pure mathematical background, the authors present a variety of powerful techniques, including the use of the operator-valued Poisson kernel, various forms of the functional calculus, Hardy spaces, fixed point theorems, minimal vectors, universal operators and moment sequences. The subject is presented at a level accessible to postgraduate students, as well as established researchers. It will be of particular interest to those who study linear operators and also to those who work in other areas of pure mathematics.

Author : Anatoliy Malyarenko
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 53,9 Mb
Release : 2012-10-26
Category : Mathematics
ISBN : 9783642334061

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Invariant Random Fields on Spaces with a Group Action by Anatoliy Malyarenko Pdf

The author describes the current state of the art in the theory of invariant random fields. This theory is based on several different areas of mathematics, including probability theory, differential geometry, harmonic analysis, and special functions. The present volume unifies many results scattered throughout the mathematical, physical, and engineering literature, as well as it introduces new results from this area first proved by the author. The book also presents many practical applications, in particular in such highly interesting areas as approximation theory, cosmology and earthquake engineering. It is intended for researchers and specialists working in the fields of stochastic processes, statistics, functional analysis, astronomy, and engineering.

Author : Radu Zaharopol
Publisher : Springer Science & Business Media
Page : 1008 pages
File Size : 55,7 Mb
Release : 2005-01-28
Category : Mathematics
ISBN : 376437134X

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Invariant Probabilities of Markov-Feller Operators and Their Supports by Radu Zaharopol Pdf

This book covers invariant probabilities for a large class of discrete-time homogeneous Markov processes known as Feller processes. These Feller processes appear in the study of iterated function systems with probabilities, convolution operators, and certain time series. From the reviews: "A very useful reference for researchers wishing to enter the area of stationary Markov processes both from a probabilistic and a dynamical point of view." --MONATSHEFTE FÜR MATHEMATIK

Author : Onésimo Hernández-Lerma,Jean B. Lasserre
Publisher : Birkhäuser
Page : 213 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880244

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Markov Chains and Invariant Probabilities by Onésimo Hernández-Lerma,Jean B. Lasserre Pdf

This book is about discrete-time, time-homogeneous, Markov chains (Mes) and their ergodic behavior. To this end, most of the material is in fact about stable Mes, by which we mean Mes that admit an invariant probability measure. To state this more precisely and give an overview of the questions we shall be dealing with, we will first introduce some notation and terminology. Let (X,B) be a measurable space, and consider a X-valued Markov chain ~. = {~k' k = 0, 1, ... } with transition probability function (t.pJ.) P(x, B), i.e., P(x, B) := Prob (~k+1 E B I ~k = x) for each x E X, B E B, and k = 0,1, .... The Me ~. is said to be stable if there exists a probability measure (p.m.) /.l on B such that (*) VB EB. /.l(B) = Ix /.l(dx) P(x, B) If (*) holds then /.l is called an invariant p.m. for the Me ~. (or the t.p.f. P).

Author : John Christopher Taylor
Publisher : American Mathematical Soc.
Page : 220 pages
File Size : 45,5 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 0821870246

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Topics in Probability and Lie Groups by John Christopher Taylor Pdf

This volume is comprised of two parts: the first contains articles by S. N. Evans, F. Ledrappier, and Figa-Talomanaca. These articles arose from a Centre de Recherches de Mathematiques (CRM) seminar entitiled, ''Topics in Probability on Lie Groups: Boundary Theory''. Evans gives a synthesis of his pre-1992 work on Gaussian measures on vector spaces over a local field. Ledrappier uses the freegroup on $d$ generators as a paradigm for results on the asymptotic properties of random walks and harmonic measures on the Martin boundary. These articles are followed by a case study by Figa-Talamanca using Gelfand pairs to study a diffusion on a compact ultrametric space. The second part of the book is an appendix to the book Compactifications of Symmetric Spaces (Birkhauser) by Y. Guivarc'h and J. C. Taylor. This appendix consists of an article by each author and presents the contents of this book in a more algebraic way. L. Ji and J.-P. Anker simplifies some of their results on the asymptotics of the Green function that were used to compute Martin boundaries. And Taylor gives a self-contained account of Martin boundary theory for manifolds using the theory of second order strictly elliptic partial differential operators.

Author : Niels Jacob
Publisher : De Gruyter Akademie Forschung
Page : 218 pages
File Size : 54,8 Mb
Release : 1996
Category : Mathematics
ISBN : UOM:39015040997887

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Pseudo-differential Operators and Markov Processes by Niels Jacob Pdf

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Page : 1885 pages
File Size : 51,8 Mb
Release : 2011-10-05
Category : Mathematics
ISBN : 9781461418054

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Mathematics of Complexity and Dynamical Systems by Robert A. Meyers Pdf

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.