Invariant Markov Processes Under Lie Group Actions - Hardcover

Liao, Ming

 
9783319923239: Invariant Markov Processes Under Lie Group Actions
Hardcover
ISBN 10: 3319923234 ISBN 13: 9783319923239
Verlag: Springer, 2018

Inhaltsangabe

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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Von der hinteren Coverseite

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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
2018
Sprache
Englisch
ISBN 10 
3319923234
ISBN 13 
9783319923239
Einband
Gebundene Ausgabe
Auflage
1
Anzahl der Seiten
376
Kontakt zum Hersteller
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Deutschland

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Vorgestellte Ausgabe

ISBN 10:  3030064069 ISBN 13:  9783030064068
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Softcover