Methods and Applications of Analysis

Volume 9 (2002)

Number 3

Limiting Behaviors for Brownian Motion Reflected on Brownian Motion

Pages: 377 – 392

DOI: http://dx.doi.org/10.4310/MAA.2002.v9.n3.a5

Authors

Xia Chen

Wenbo V. Li

Abstract

Suppose that g(t) and Wt are independent Brownian motions starting from g(0) = W0 = 0. Consider the Brownian motion Yt reflected on g(t), obtained from Wt by the means of the Skorohod lemma. The upper and lower limiting behaviors of Yt are presented. The upper tail estimate on exit time is computed via principal eigenvalue.

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