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Weak convergence of laws of stochastic processes on Riemannian manifolds
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  • Published: April 2001

Weak convergence of laws of stochastic processes on Riemannian manifolds

  • Yukio Ogura1 

Probability Theory and Related Fields volume 119, pages 529–557 (2001)Cite this article

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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.

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Authors and Affiliations

  1. Department of Mathematics, Saga University, Saga, 840-8502, Japan. e-mail: ogura@ms.saga-u.ac.jp, , , , , , JP

    Yukio Ogura

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  1. Yukio Ogura
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Received: 22 February 2000¶Published online: 9 March 2001

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Ogura, Y. Weak convergence of laws of stochastic processes on Riemannian manifolds. Probab Theory Relat Fields 119, 529–557 (2001). https://doi.org/10.1007/PL00008770

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  • Issue Date: April 2001

  • DOI: https://doi.org/10.1007/PL00008770

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  • Mathematics Subject Classification (2000): 58J65, 60F17
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