Weak convergence of laws of stochastic processes on Riemannian manifolds |
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Authors: | Yukio Ogura |
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Institution: | (1) Department of Mathematics, Saga University, Saga, 840-8502, Japan. e-mail: ogura@ms.saga-u.ac.jp, JP |
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Abstract: | Weak convergence of the laws of discrete time re-metrized stochastic processes derived from Brownian motions on compact Riemannian
manifolds with heat kernels uniformly bounded by a constant on each compact set of the time parameter and bounded volumes
to a stochastic process is given. With a weak condition, we also give weak convergence of those of Brownian motions themselves
on manifolds in the same class. Several examples are given, which cover the cases when the manifolds collapse, the cases when
the original Brownian motions converge to a non-local Markov process, and the cases when the Gromov-Hausdorff limit and the
spectral limit by Kasue and Kumura are different.
Received: 22 February 2000?Published online: 9 March 2001 |
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Keywords: | Mathematics Subject Classification (2000): 58J65 60F17 |
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