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

Kiyoshi Kawazu, Yuki Suzuki

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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. Ã, and B̃t, both having probability 1/2, in such a way that our diffusion process X(t) exhibits quite different limiting behavior depending on whether it is conditioned on Ãt or on B̃t (t → ∞). The asymptotic behavior of the maximum process of X(t) is also investigated. Our results improve those of Kawazu, Suzuki, and Tanaka (2001).

Original languageEnglish
Pages (from-to)997-1012
Number of pages16
JournalJournal of Applied Probability
Issue number4
Publication statusPublished - 2006 Dec


  • Diffusion process
  • Occupation time
  • Random environment

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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