Some Asymptotic Formulas for a Brownian Motion from The Maximum and Minimum Domains with Regular Varying Boundary

Dawei Lu

Communications in Statistics - Theory and Methods, 2014, vol. 43, issue 18, 3848-3865

Abstract: Consider a Brownian motion starting at an interior point of the maximum or minimum domains with regular varying boundary, namely, Dmax = {(x, y1, y2): ‖x‖ t)$\log P(\tau _{D_{\max }}>t)$ and logP(τDmin>t)$\log P(\tau _{D_{\min }}>t)$ are given as t → ∞, depending on the relationship between f1 and f2, respectively. The proof methods are based on Gordon’s inequality and early works of Li, Lifshits, and Shi in the single general domain case.

Date: 2014
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DOI: 10.1080/03610926.2012.702364

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