Exit times densities of the Bessel process

Abstract

We examine the density functions of the first exit times of the Bessel process from the intervals [0, 1) and (0, 1). First, we express them by means of the transition density function of the killed process. Using that relationship we provide precise estimates and asymptotics of the exit time densities. In particular, the results hold for the first exit time of the n-dimensional Brownian motion from a ball.2010 Mathematics Subject Classification. 60J60, 60J65.

Dirichlet Heat Kernel for the Laplacian in a Ball

“…This extends estimates from [12], where the exit time (without its dependence on exit place) density from the ball was discussed.…”

Asymptotic behaviour of the Bessel heat kernels

“…In this context, providing asymptotic expansion of the considered Bessel heat kernels is a natural improvement of these results. It is worth noting that the analogous expansions for the density of the first hitting time of Bessel processes were derived recently in [17] and [15].…”

Asymptotic behaviour of the Bessel heat kernels

“…In this context, providing asymptotic expansion of the considered Bessel heat kernels is a natural improvement of these results. It is worth noting that the analogous expansions for the density of the first hitting time of Bessel processes were derived recently in [15,17].…”