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Invariant Markov processes under Lie Group actions

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Invariant Markov processes under Lie Group actions/ by Ming Liao.
作者:	Liao, Ming.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	xiii, 363 p. :digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Probabilities. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-92324-6
ISBN:	9783319923246

Invariant Markov processes under Lie Group actions
Liao, Ming.

Invariant Markov processes under Lie Group actions[electronic resource] /by Ming Liao. - Cham :Springer International Publishing :2018. - xiii, 363 p. :digital ;24 cm.

Invariant 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.

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 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 G A 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.

ISBN: 9783319923246

Standard No.: 10.1007/978-3-319-92324-6doiSubjects--Topical Terms:

527847
Probabilities.

LC Class. No.: QA274 / .L536 2018

Dewey Class. No.: 519.2

Invariant Markov processes under Lie Group actions
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520 $a 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 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 G A 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.
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