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An invariance principle for non-symmetric Markov processes and reflecting diffusions in random domains
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  • Published: March 1995

An invariance principle for non-symmetric Markov processes and reflecting diffusions in random domains

  • Hirofumi Osada1 &
  • Toshifumi Saitoh1 

Probability Theory and Related Fields volume 101, pages 45–63 (1995)Cite this article

  • 148 Accesses

  • 14 Citations

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Summary

We study an invariance principle for additive functionals of nonsymmetric Markov processes with singular mean forward velocities. We generalize results of Kipnis and Varadhan [KV] and De Masi et al. [De] in two directions: Markov processes are non-symmetric, and mean forward velocities are distributions. We study continuous time Markov processes. We use our result to homogenize non-symmetric reflecting diffusions in random domains.

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References

  • [B] Bhattacharya, R.: A central limit theorem for diffusions with periodic coefficients. Ann. Prob.13, 385–396 (1985)

    Google Scholar 

  • [D] Davies, E.B.: Explicit constants for Gaussian upper bounds on heat kernels. Am. J. Math.109, 319–334 (1987)

    Google Scholar 

  • [De] De Masi, A. et al.: An invariance principle for reversible Markov processes. Applications to random motions in random environments. J. Stat. Phys.55, 787–855 (1989)

    Google Scholar 

  • [F1] Fukushima, M.: A construction of reflecting barrier Brownian motions for bounded domains. Osaka J. Math.4, 183–215 (1967)

    Google Scholar 

  • [F2] Fukushima, M.: Dirichlet forms and Markov processes. North-Holland: Kodansha 1980

    Google Scholar 

  • [H] Helland, I.S.: Central limit theorems for martingales with discrete or continuous time. Scand. J. Stat. 979–994 (1982)

  • [IW] Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes, 2nd ed., North-Holland: Kodansha 1989

    Google Scholar 

  • [Ki] Kim, J.H.: Stochastic calculus related to non-symmetric Dirichlet forms. Osaka J. Math.24, 331–371 (1987)

    Google Scholar 

  • [Ko] Kozlov, S.M. et al.: Averaging and G-convergence of differential operators. Russian Math. Survey34(5), 69–147 (1979)

    Google Scholar 

  • [KV] Kipnis, C., Varadhan, S.R.S.: Central limit theorems for additive functional of reversible Markov process and applications to simple exclusions. Commun. Math. Phys.104, 1–19 (1986)

    Google Scholar 

  • [MR] Ma, Z., Röckner: Introduction to the theory of (non-symmetric) Dirichlet forms Berlin Heidelberg New York: Springer 1992

    Google Scholar 

  • [Oc] Ochi, Y.: Limit theorems for a class of diffusion processes. Stochastics15, 251–269 (1985)

    Google Scholar 

  • [Oe] Oelshlager, K.: Homogenization of a diffusion process in a divergence-free random field. Ann. Probab.16, 1084–1126 (1988)

    Google Scholar 

  • [O1] Osada, H.: Homogenization of diffusion processes with random stationary coefficients. In: Proc. 4th Japan-USSR Symp. Prob. Theo. (Lect. Notes Math., vol. 1021 pp. 507–517) Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  • [O2] Osada, H.: Homogenization of reflecting barrier Brownian motions. In: Proc. Taniguchi Workshop at Sanda and Kyoto (1990) (Pitman Research notes in Math. vol. 283 pp. 59–74) Longman 1993

  • [Os] Oshima, Y.: Lecture on Dirichlet spaces. Univ. Erlangen-Nurnberg 1988

  • [PV] Papanicolaou, G.C., Varadhan, S.R.S.: Boundary value problem with rapidly oscillating random coefficients. Colloq. Math. Soc. Janos Bolyai27, 835–873 (1979)

    Google Scholar 

  • [RY] Revuz, D., Yor, M.: Continuous martingales and Brownian motion. Berlin Heidelberg New York: Springer 1991

    Google Scholar 

  • [T] Tanemura, T.: Homogenization of a reflecting barrier Brownian motion in a continuum percolation cluster inR d to appear in Kodai Math. Journal.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Tokyo, 7-3-1 Hongo, Tokyo, 113, Japan

    Hirofumi Osada & Toshifumi Saitoh

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  1. Hirofumi Osada
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  2. Toshifumi Saitoh
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Osada, H., Saitoh, T. An invariance principle for non-symmetric Markov processes and reflecting diffusions in random domains. Probab. Th. Rel. Fields 101, 45–63 (1995). https://doi.org/10.1007/BF01192195

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  • Received: 07 September 1993

  • Revised: 21 June 1994

  • Issue Date: March 1995

  • DOI: https://doi.org/10.1007/BF01192195

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Mathematics Subject Classification (1991)

  • 60J55
  • 60J60
  • 35K99
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