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1 results

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

  • Part of
  • Kiyoshi Kawazu, Yuki Suzuki
  • Journal:
    Journal of Applied Probability / Volume 43 / Issue 4 / December 2006
    Published online by Cambridge University Press:
    14 July 2016, pp. 997-1012
    Print publication:
    December 2006
    • Article
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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).