Cone exponents of Brownian motions with particular drifts

Izumi Okada

doi:10.30757/ALEA.V16-31

Cone exponents of Brownian motions with particular drifts

Izumi Okada

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Herein, we describe multidimensional Brownian motions for d = 2; 3 with drifts whose order is the same as that of the mean displacement of a Brownian motion. We consider the probabilities that the processes remain in specific cones for a considerable amount of time. We obtain exponents expressing the probabilities, which are different from that of the ordinary Brownian motion. Finally, we suggest an open problem concerning the exact values.

Original language	English
Pages (from-to)	855-870
Number of pages	16
Journal	Alea
Volume	16
Issue number	1
DOIs	https://doi.org/10.30757/ALEA.V16-31
Publication status	Published - 2019

All Science Journal Classification (ASJC) codes

Statistics and Probability

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abstract = "Herein, we describe multidimensional Brownian motions for d = 2; 3 with drifts whose order is the same as that of the mean displacement of a Brownian motion. We consider the probabilities that the processes remain in specific cones for a considerable amount of time. We obtain exponents expressing the probabilities, which are different from that of the ordinary Brownian motion. Finally, we suggest an open problem concerning the exact values.",

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