---

＜電子ブック＞
Invariant Markov Processes Under Lie Group Actions / by Ming Liao

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2018
大きさ	XIII, 363 p : online resource
著者標目	*Liao, Ming author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Topological groups LCSH:Lie groups LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) FREE:Probability Theory FREE:Topological Groups and Lie Groups FREE:Global Analysis and Analysis on Manifolds
一般注記	Invariant Markov processes under actions of topological groups -- Lévy processes in Lie groups -- Lévy processes in homogeneous spaces -- Lévy processes in compact Lie groups -- Spherical transform and Lévy-Khinchin formula -- Inhomogeneous Lévy processes in Lie groups -- Proofs of main results -- Inhomogenous Lévy processes in homogeneous spaces -- Decomposition of Markov processes -- Appendices -- Bibliography -- Index 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 G A 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 HTTP:URL=https://doi.org/10.1007/978-3-319-92324-6

 類似資料