UID:
almahu_9947921560202882
Format:
V, 105 p.
,
online resource.
ISBN:
9783540470229
Series Statement:
Lecture Notes in Mathematics, 1720
Content:
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.
Note:
Construction of connections -- The infinitesimal generators and associated operators -- Decomposition of noise and filtering -- Application: Analysis on spaces of paths -- Stability of stochastic dynamical systems -- Appendices.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9783540667087
Language:
English
Subjects:
Mathematics
URL:
http://dx.doi.org/10.1007/BFb0103064
URL:
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