Asymptotics of the densities of the first passage time distributions for Bessel diffusions

Uchiyama, Kôhei

doi:10.1090/S0002-9947-2014-06155-2

Asymptotics of the densities of the first passage time distributions for Bessel diffusions
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Trans. Amer. Math. Soc. 367 (2015), 2719-2742 Request permission

Abstract:

This paper concerns the first passage times to a point $a >0$, denoted by $\sigma _a$, of Bessel processes. We are interested in the case when the process starts at $x>a$ and we compute the densities of the distributions of $\sigma _a$ to obtain the exact asymptotic forms of them as $t\to \infty$ that are valid uniformly in $x>a$ for every order of the Bessel process.

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