The first exit time of fractional Brownian motion from an unbounded domain

Yinbing Zhou and Dawei Lu

Statistics & Probability Letters, 2025, vol. 218, issue C

Abstract: Consider a fractional Brownian motions starting at the interior point x0,h‖x0‖+2K∈Rd+1 with the constant K>1, for some fixed x0∈Rd, of an unbounded domain D=x,y∈Rd+1:y>h‖x‖, The function h is a nondecreasing, lower semicontinuous, and convex function on [0,∞) with h(0) being finite. Here we take h−1x=Axαlogxβwith a positive constant A for x>K. It is evident that h−1(x) exhibits monotonic behavior for sufficiently large values of x. Let τD denote the first time that the fractional Brownian motion exits from D. In most cases, we give the asymptotically equivalent estimate of logPτD>t. The proof methods are based on the earlier works of Li, Shi, Lifshits, and Aurzada.

Keywords: Exit time; Fractional Brownian motion; Small ball probability; Large deviation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2024.110319

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