The First Exit Time of Fractional Brownian Motion with a Drift from a Parabolic Domain

Yinbing Zhou () and Dawei Lu ()
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Yinbing Zhou: Dalian University of Technology
Dawei Lu: Dalian University of Technology

Methodology and Computing in Applied Probability, 2024, vol. 26, issue 1, 1-19

Abstract: Abstract We study the first exit time of a fractional Brownian motion with a drift from a parabolic domain. Actually, we explore three different regimes. In the first regime, the role of drift is negligible. In the second regime, the role of drift is dominating. The behavior of exit probability is the same as that of the crossing probability of a certain moving non-random boundary. In particular, the most interesting, intermediate regime, where all factors come into play, has been solved in this paper. Finally, numerical simulations are conducted, providing an approximate range for the asymptotic estimates to illustrate the practical implications and potential applications of our main results.

Keywords: Exit time; Fractional Brownian motion; Small ball probability; Large deviation; 60G15; 60G40; 60F10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11009-024-10074-1

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