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arXiv · 1412.0360

Recurrence of the Brownian motion in multidimensional semi-selfsimilar environments and Gaussian environments

Seiichiro Kusuoka·Hiroshi Takahashi·Yozo Tamura
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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 multidimensional 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.

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Seiichiro Kusuoka, Hiroshi Takahashi, Yozo Tamura. 2015-07-11. Recurrence of the Brownian motion in multidimensional semi-selfsimilar environments and Gaussian environments. https://doi.org/10.1007/s11118-015-9492-3

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