The first exit time of fractional Brownian motion from the minimum and maximum parabolic domains

Dawei Lu and Yinbing Zhou

Statistics & Probability Letters, 2022, vol. 186, issue C

Abstract: Consider a fractional Brownian motion starting at an interior point of the minimum and maximum parabolic domains, namely, Dmin=x,y1,y2:‖x‖0, and p1,p2>1. Let τmin and τmax denote the first times that the fractional Brownian motion exits from Dmin and Dmax, respectively. Asymptotically equivalent estimates of logPτmin>t and logPτmax>t are respectively given by using Gordon’s inequality, depending on the relationship between p1 and p2. The proof methods are based on early works of Li, Shi, Lifshits, Aurzada and Lu.

Keywords: Exit time; Fractional Brownian motion; Gordon’s inequality; Small deviations (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2022.109467

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