Recurrence of the Brownian Motion in Multidimensional Semi-selfsimilar Environments and Gaussian Environments

Seiichiro Kusuoka, Hiroshi Takahashi, Yozo Tamura

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Asymptotic behavior of the one-dimensional Brownian motion in general random environments has been investigated by many researchers. However, many of the methods used in the argument are available only for the one-dimensional case. In this paper the multi-dimensional case of the problem is considered, and we obtain some sufficient conditions for recurrence of the multi-dimensional Brownian motion in random environments. By using the sufficient conditions we show that the recurrence of the Brownian motion in Gaussian environments under some conditions on the correlation functions.

Original languageEnglish
Pages (from-to)695-705
Number of pages11
JournalPotential Analysis
Volume43
Issue number4
DOIs
Publication statusPublished - 2015 Nov 1

Keywords

  • Diffusion process
  • Fractional Brownian field
  • Gaussian field
  • Random environment
  • Recurrence

ASJC Scopus subject areas

  • Analysis

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