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On the Geometry of Diffusion Operators and Stochastic Flows (Paperback, 1999 ed.)
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On the Geometry of Diffusion Operators and Stochastic Flows (Paperback, 1999 ed.)
Series: Lecture Notes in Mathematics, 1720
Expected to ship within 10 - 15 working days
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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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