On the geometry of diffusion operators and stochastic flows /
Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properti...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer,
[1999]
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| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1720. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, especially those with interests in stochastic flows, infinite dimensional analysis, or geometric analysis, and also to researchers in sub-Riemannian geometry. A basic background in differential geometry is assumed, but the construction of the connections is very direct and itself gives an intuitive and concrete introduction. Knowledge of stochastic analysis is also assumed for later chapters. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (118 pages) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliography: | Includes bibliographical references (pages [111]-116) and index. |
| ISBN: | 9783540470229 (electronic bk.) 3540470220 (electronic bk.) |
| ISSN: | 0075-8434 ; |