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On unique ergodicity for degenerate diffusions. (English) Zbl 0617.60076
From authors’ abstract: We investigate the invariant probabilities of a possibly degenerate diffusion process on a manifold. Using the support theorems of Stroock, Varadhan and Kunita, the possible candidates for supports of invariant probabilities can be characterized as the invariant control sets of the corresponding control system. There remains the problem of how many invariant probabilities can coexist on one invariant control set C. Uniqueness on C is proved under the assumption that the Lie algebra generated by the drift and diffusion vector fields is full at one point in C.
Reviewer: A.Ya.Dorogovtsev

MSC:
60J60 Diffusion processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
28C99 Set functions and measures on spaces with additional structure
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