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A large deviation result for a class of Dirichlet processes
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  • Published: June 1995

A large deviation result for a class of Dirichlet processes

  • Weian Zheng1 

Probability Theory and Related Fields volume 101, pages 237–249 (1995)Cite this article

Summary

Let λ>0 be a constant and let λ−1 <q(x) < λ be a bounded measurable function. We consider the large deviation problem for the diffusion process with generator

We are going to prove that its density function satisfies

$$\mathop {\lim }\limits_{t \to 0} t\log H(y,t,x) = - \frac{{\left| {x - y} \right|^2 }}{2}$$

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References

  1. Carlen, E., Kusuoka, S., Stroock, D.: Upper bounds for symmetric Markov transition functions. Ann. Inst. Henri Poincaré, Sup. au no. 2 (1987)

  2. Chen, Z.Q.: On reflecting diffusion processes and Skorohod decompositions. Probab. Theory Relat. Fields94 (1993)

  3. Davies, E.B.: Heat kernels and spectral theory, Cambridge: Cambridge Univ. Press (1989)

    Google Scholar 

  4. Fabes, E., Stroock, D.: A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash. Arch. Ratl. Mech. Anal.96(4), (1986).

  5. Fukushima, M.: Dirichlet forms and Markov processes. Amsterdam: North-Holland (1985)

    Google Scholar 

  6. Kusuoka, S., and Stroock, D.: Long time estimates for the heat kernel associated with a uniformly subelliptic second order operators. Ann. Math.127, (1988)

  7. Lyons, T. and Zheng, W.: A crossing estimate for the canonical process on a Dirichlet space and a tightness result. Colloque Paul Levy sur les Processus Stochastiques, Asterisque157–158, 249–271 (1988)

    Google Scholar 

  8. Norris, J.R., Stroock, D.W.: Estimates on the fundamental solution to heat flow with uniformly elliptic coefficients. Proc. London Math. Soc. (1991)

  9. Stroock, D.W.: Diffusion semigroups corresponding to uniformly elliptic divergence from operators. Sém, de Prob. XXII (Lect. Notes in Math., Vol. 1321) (1988)

  10. Varadhan, S.R.S.: On the behavior of the fundamental solution of the heat equation with variable coefficients. Comm. Pure Appl. Math.20, (1967)

  11. Zheng, W.: Diffusion processes on Lipschitz manifolds and their applications. In: Cranston, M., Pinsky, M.: Stochastic analysis, AMS Series Proc. Symp. in Pure Math. Providence, RI: Amer. Mathematical Soc. 1994

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, 92717, Irvine, CA, USA

    Weian Zheng

Authors
  1. Weian Zheng
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Additional information

Research supported by N.S.F. grant DMS-9204038

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Cite this article

Zheng, W. A large deviation result for a class of Dirichlet processes. Probab. Th. Rel. Fields 101, 237–249 (1995). https://doi.org/10.1007/BF01375827

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  • Received: 19 October 1993

  • Revised: 28 June 1994

  • Issue Date: June 1995

  • DOI: https://doi.org/10.1007/BF01375827

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Mathematics Subject Classification (1991)

  • 60J65
  • 60J60
  • 58G32
  • 58G11
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