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.
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Kusuoka, S., Takahashi, H. & Tamura, Y. Recurrence of the Brownian Motion in Multidimensional Semi-selfsimilar Environments and Gaussian Environments. Potential Anal 43, 695–705 (2015). https://doi.org/10.1007/s11118-015-9492-3
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DOI: https://doi.org/10.1007/s11118-015-9492-3