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OverviewThe 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 Levy-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 Levy 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. Full Product DetailsAuthor: Ming LiaoPublisher: Springer Nature Switzerland AG Imprint: Springer Nature Switzerland AG Edition: Softcover reprint of the original 1st ed. 2018 Weight: 0.581kg ISBN: 9783030064068ISBN 10: 3030064069 Pages: 363 Publication Date: 14 December 2018 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsInvariant Markov processes under actions of topological groups.- Levy processes in Lie groups.- Levy processes in homogeneous spaces.- Levy processes in compact Lie groups.- Spherical transform and Levy-Khinchin formula.- Inhomogeneous Levy processes in Lie groups.- Proofs of main results.- Inhomogenous Levy processes in homogeneous spaces.- Decomposition of Markov processes.- Appendices.- Bibliography.- Index.ReviewsThe author ... has published this text for readers who have advanced knowledge of Lie groups, actions of Lie groups (a central theme in mathematics and statistics) and homogeneous spaces, stochastic processes, stochastic integrals, stochastic differential equations, diffusion processes, martingales, and Poisson measures, covered briefly in the appendices. ... the author describes many avenues for further research. (Nirode C. Mohanty, zbMATH 1460.60001, 2021) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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