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Weak convergence of symmetric diffusion processes
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  • Published: October 1997

Weak convergence of symmetric diffusion processes

  • Kazuhiro Kuwae1 &
  • Toshihiro Uemura2 

Probability Theory and Related Fields volume 109, pages 159–182 (1997)Cite this article

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Summary.

In this paper, we show the convergence of forms in the sense of Mosco associated with the part form on relatively compact open set of Dirichlet forms with locally uniform ellipticity and the locally uniform boundedness of ground states under regular Dirichlet space setting. We also get the same assertion under Dirichlet space in infinite dimensional setting. As a result of this, we get the weak convergence under some conditions on initial distributions and the growth order of the volume of the balls defined by (modified) pseudo metric used in K. Th. Sturm.

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Authors and Affiliations

  1.  Department of Information Science, Faculty of Science and Engineering, Saga University, Saga, Japan. e-mail: kuwae@gauss.ma.is.saga-u.ac.jp, , , , , , JP

    Kazuhiro Kuwae

  2.  Department of Mathematical Science, Faculty of Engineering Science, Osaka University, Osaka, Japan. email: uemura@kobe.kobeuc.ac.jp, , , , , , JP

    Toshihiro Uemura

Authors
  1. Kazuhiro Kuwae
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  2. Toshihiro Uemura
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Received: 18 September 1995 / In revised form: 23 January 1997

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Kuwae, K., Uemura, T. Weak convergence of symmetric diffusion processes. Probab Theory Relat Fields 109, 159–182 (1997). https://doi.org/10.1007/s004400050129

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  • Issue Date: October 1997

  • DOI: https://doi.org/10.1007/s004400050129

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  • AMS Subject Classification (1991): 31C25
  • 60Y60
  • 60F05
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