Some Asymptotic Formulas for a Brownian Motion From the Maximum and Minimum Complicated Domains

Dawei Lu

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 15, 3192-3217

Abstract: Consider a Brownian motion with drift starting at an interior point of the minimum or maximum parabolic domains, namely, Dmin=x,y1,y2:∥x∥ t)${\it log} P(\tau _{D_{min}}>t)$ and logP(τDmax>t)${\it log} P(\tau _{D_{max}}>t)$ are given as t → ∞, depending on the relationship among pj, rj, j = 1, 2, respectively. The proofs are based on Gordon’s inequality.

Date: 2015
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DOI: 10.1080/03610926.2013.823210

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