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We consider the quasi-stationary distribution of the classical Shiryaevdiffusion restricted to the interval $[0,A]$ with absorption at a fixed $A>0$.We derive analytically a closed-form formula for the distribution's fractionalmoment of an {\em arbitrary} given order $s\in\mathbb{R}$; the formula isconsistent with that previously found by Polunchenko and Pepelyshev (2018) forthe case of $s\in\mathbb{N}$. We also show by virtue of the formula that, if$s<1$, then the $s$-th fractional moment of the quasi-stationary distributionbecomes that of the exponential distribution (with mean $1/2$) in the limit as$A\to+\infty$; the limiting exponential distribution is the stationarydistribution of the reciprocal of the Shiryaev diffusion.

Analytic Evaluation of the Fractional Moments for the Quasi-Stationary Distribution of the Shiryaev Martingale on an Interval