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 - Nov 1 2015

    Keywords

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

    ASJC Scopus subject areas

    • Analysis

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