Some asymptotic formulas of a Brownian motion with regular variation from the maximum and minimum complicated domains

Dawei Lu

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 22, 6569-6595

Abstract: Consider the following domains: Dmin={(x,y1,y2):∥x∥ t)$\log P(\tau _{D_{\!min}}>t)$ and logP(τDmax>t)$\log P(\tau _{D_{max}}>t)$ are given for t → ∞, depending on the relationship among pj, and regular variations hj, j = 1, 2, respectively. The proofs are based on Gordon's inequality.

Date: 2016
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DOI: 10.1080/03610926.2014.960590

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