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SOME LIMIT THEOREMS RELATED TO MULTI-DIMENSIONAL DIFFUSIONS IN A RANDOM ENVIRONMENT
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 Title & Authors
SOME LIMIT THEOREMS RELATED TO MULTI-DIMENSIONAL DIFFUSIONS IN A RANDOM ENVIRONMENT
Kim, Dae-Hong;
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 Abstract
In this paper, we consider a multi-dimensional diffusion process in a self-similar random environment and prove a limit theorem for the shape of the full trajectory of the diffusion by using the localization phenomenon.
 Keywords
Dirichlet forms;random environment;set valued diffusion processes;subdiffusivity;
 Language
English
 Cited by
1.
Recurrence of the Brownian Motion in Multidimensional Semi-selfsimilar Environments and Gaussian Environments, Potential Analysis, 2015, 43, 4, 695  crossref(new windwow)
 References
1.
T. Brox, A one-dimensional diffusion process in a Wiener medium, Ann. Probab. 14 (1986), no. 4, 1206-1218. crossref(new window)

2.
M. Fukushima, Y. Oshima, and M. Takeda, Dirichlet Forms and Symmetric Markov Processes, de Gruyter Studies in Mathematics, 19. Walter de Gruyter & Co., Berlin, 1994.

3.
M. Fukushima and H. Tanaka, Poisson point processes attached to symmetric diffusions, Ann. Inst. H. Poincare Probab. Statist. 41 (2005), no. 3, 419-459. crossref(new window)

4.
R. A. Holley, S. Kusuoka, and D. W. Stroock, Asymptotics of the spectral gap with applications to the theory of simulated annealing, J. Funct. Anal. 83 (1989), no. 2, 333-347. crossref(new window)

5.
K. Kawazu, Y. Tamura, and H. Tanaka, Limit theorems for one-dimensional diffusions and random walks in random environments, Probab. Theory Related Fields 80 (1989), no. 4, 501-541. crossref(new window)

6.
D. Kim, On spectral gaps and exit time distributions for a non-smooth domain, Forum Math. 18 (2006), no. 4, 571-583. crossref(new window)

7.
D. Kim and Y. Oshima, Some inequalities related to transience and recurrence of Markov processes and their applications, J. Theor. Probab. 23 (2010), no. 1, 148-168. crossref(new window)

8.
P. Mathieu, Zero white noise limit through Dirichlet forms, with application to diffusions in a random medium, Probab. Theory Related Fields 99 (1994), no. 4, 549-580. crossref(new window)

9.
P. Mathieu, Limit theorems for diffusions with a random potential, Stochastic Process. Appl. 60 (1995), no. 1, 103-111. crossref(new window)

10.
Y. G. Sinai, The limit behavior of a one-dimensional random walk in a random environment, Teor. Veroyatnost. i Primenen. 27 (1982), no. 2, 247-258.

11.
P. Stollmann and J. Voigt, Perturbation of Dirichlet forms by measures, Potential Anal. 5 (1996), no. 2, 109-138. crossref(new window)

12.
H. Takahashi, Recurrence and transience of multi-dimensional diffusion processes in reflected Brownian environments, Statist. Probab. Lett. 69 (2004), no. 2, 171-174. crossref(new window)

13.
H. Tanaka, Recurrence of a diffusion process in a multidimensional Brownian environment, Proc. Japan Acad. Ser. A Math. Sci. 69 (1993), no. 9, 377-381. crossref(new window)