Authors:
Author is an internationally recognized leader in the study of jump processes in stochastic differential geometry
Presents new research involving the interaction of several mathematical areas, such as stochastic analysis, differential geometry, Lie groups, measure theory, and harmonic analysis
Explores an intersection of probability theory and Lie group theory with potential for many future applications
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Table of contents (9 chapters)
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Front Matter
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Back Matter
About this book
— 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.
Reviews
“The 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)
Authors and Affiliations
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Department of Mathematics and Statistics, Auburn University, Auburn, USA
Ming Liao
Bibliographic Information
Book Title: Invariant Markov Processes Under Lie Group Actions
Authors: Ming Liao
DOI: https://doi.org/10.1007/978-3-319-92324-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-92323-9Published: 17 July 2018
Softcover ISBN: 978-3-030-06406-8Published: 14 December 2018
eBook ISBN: 978-3-319-92324-6Published: 28 June 2018
Edition Number: 1
Number of Pages: XIII, 363
Topics: Probability Theory and Stochastic Processes, Topological Groups, Lie Groups, Global Analysis and Analysis on Manifolds