Analytic moment and Laplace transform formulae for the quasi-stationary distribution of the Shiryaev diffusion on an interval

TL;DR

This paper derives explicit formulas for the moments and Laplace transforms of the quasi-stationary distribution of the Shiryaev diffusion on a bounded interval, aiding understanding of its long-term behavior.

Contribution

It provides the first closed-form analytic expressions for the moments and Laplace transforms of the quasi-stationary distribution of the Shiryaev diffusion on an interval.

Findings

Closed-form formulas for moments

Explicit Laplace transform expressions

Enhanced understanding of Shiryaev diffusion behavior

Abstract

We derive analytic closed-form moment and Laplace transform formulae for the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval $[0,A]$ with absorption at a given $A>0$.