Moments and tails of hitting times of Bessel processes and convolutions of elementary mixtures of exponential distributions

TL;DR

This paper provides explicit tail estimates and moments for hitting times of Bessel processes, derived from general estimates for convolutions of elementary mixtures of exponential distributions, advancing understanding of their probabilistic behavior.

Contribution

It introduces new explicit tail and moment estimates for Bessel process hitting times based on convolutions of exponential mixtures, a novel analytical approach.

Findings

Explicit tail bounds for Bessel process hitting times.

Exact estimates for moments of hitting times.

General estimates for convolutions of exponential mixtures.

Abstract

We present explicit estimates of right and left tails and exact (up to universal, multiplicative constants) estimates of tails and moments of hitting times of Bessel processes. The latter estimates are obtained from more general estimates of moments and tails established for convolutions of elementary mixtures of exponential distributions.