Analytic Evaluation of the Fractional Moments for the Quasi-Stationary Distribution of the Shiryaev Martingale on an Interval
| Autor: | Li, Kexuan, Polunchenko, Aleksey S., Pepelyshev, Andrey |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval $[0,A]$ with absorption at a fixed $A>0$. We derive analytically a closed-form formula for the distribution's fractional moment of an {\em arbitrary} given order $s\in\mathbb{R}$; the formula is consistent with that previously found by Polunchenko and Pepelyshev (2018) for the 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 distribution becomes that of the exponential distribution (with mean $1/2$) in the limit as $A\to+\infty$; the limiting exponential distribution is the stationary distribution of the reciprocal of the Shiryaev diffusion. Comment: Accepted for publication in Communications in Statistics - Simulation and Computation. arXiv admin note: text overlap with arXiv:1805.07580 |
| Databáze: | arXiv |
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