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Weak convergence of laws of stochastic processes on Riemannian manifolds. (English) Zbl 0983.58017

The author considers a sequence of Riemannian manifolds endowed with smooth measures, and the corresponding Dirichlet forms and symmetric continuous diffusions. He considers adequate topologies on the set of manifolds, and studies the weak convergence of the sequence of diffusions. However, they do not always converge, so he rather considers a sequence of time-discretized diffusions, and proves the weak convergence for the Skorokhod topology; he also gives conditions under which the limit is continuous. Then the results are improved in the case of compact manifolds, the Ricci curvatures of which are uniformly bounded from below. Several examples are given.

MSC:

58J65 Diffusion processes and stochastic analysis on manifolds
60F17 Functional limit theorems; invariance principles
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