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Limit theorems for a diffusion process with a one-sided Brownian potential

Part of:Special processesMarkov processes

Published online by Cambridge University Press:  14 July 2016

Kiyoshi Kawazu and
Yuki Suzuki
Kiyoshi Kawazu*
Affiliation:
Yamaguchi University
Yuki Suzuki*
Affiliation:
Keio University
*
∗ Postal address: Department of Mathematics, Faculty of Education, Yamaguchi University, Yoshida, Yamaguchi, 753-8513, Japan.
∗∗ Postal address: School of Medicine, Keio University, Hiyoshi, Kouhoku-ku, Yokohama, 223-8521, Japan. Email address: yuki@hc.cc.keio.ac.jp
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Abstract

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We consider a diffusion process X(t) with a one-sided Brownian potential starting from the origin. The limiting behavior of the process as time goes to infinity is studied. For each t > 0, the sample space describing the random potential is divided into two parts, à t and B̃ t , both having probability ½, in such a way that our diffusion process X(t) exhibits quite different limiting behavior depending on whether it is conditioned on à t or on B̃ t (t → ∞). The asymptotic behavior of the maximum process of X(t) is also investigated. Our results improve those of Kawazu, Suzuki, and Tanaka (2001).

Keywords

Random environmentdiffusion processoccupation time

MSC classification

Primary:60J60: Diffusion processes60K37: Processes in random environments

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 4 , December 2006, pp. 997 - 1012
Copyright
© Applied Probability Trust 2006 

References

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