Tail probability of the hitting time of Brownian motion to a sphere with fixed hitting sites
Year: 2025
Type: article
Abstract: We consider \(d\)-dimensional Brownian motion \(\{B_\mu(t)\}_{t\geqq0}\) with a drift \(\mu\in\mathbb{R}^d\) and the first hitting time \(\sigma_{r,\mu}^{(d)}\) to the sphere with radius \(r\) centered at the origin. This article deals with asymptotic behavior of the probability that both \(t\lt\sigma_{r,\mu}^{(d)}\lt\infty\) and \(B_\mu(\sigma_{r,\mu}^{(d)})\in A\) occur simultaneously, and we obtain that this probability admits an asymptotic expansion in powers of \(1/t\) if \(d\geqq3\) and in that of \(1/\log t\) if \(d=2\) for large \(t\). Moreover, we investigate the case of Brownian motion with no drift.
Source: Opuscula Mathematica
Author: Yuji Hamana
Institution: University of Tsukuba
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4412440131