Invariant Markov Processes Under Lie Group Actions. 1st ed. 2018

種類:

電子ブック

責任表示:

by Ming Liao

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Liao, Ming.
• SpringerLink (Online service)

ISBN:

9783319923246 [3319923242]    

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

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