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Stochastic flows on Riemannian manifolds. (English) Zbl 0758.58035
Diffusion processes and related problems in analysis, Vol. II: Stochastic flows, Proc. Conf. Charlotte/NC (USA) 1990, Prog. Probab. 27, 37-72 (1992).
[For the entire collection see Zbl 0742.00084.]
This article offers an elegant survey of the global analytic approach to stochastic flows on manifolds, emphasizing the heat equation for differential forms. Contents include: description of various semigroups of differential forms obtained using derivatives of stochastic flows; gradient flows; canonical, Ricci, and Hessian flows; moment exponents and topological obstructions to stability. Alternative expressions for the heat kernel for closed one-forms are given.
Reviewer: R.Darling

MSC:
58J65 Diffusion processes and stochastic analysis on manifolds
60H20 Stochastic integral equations
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