Analytic evaluation of the fractional moments for the quasi-stationary distribution of the shiryaev martingale on an interval

Li, Kexian, Polunchenko, Aleksey and Pepelyshev, Andrey ORCID: https://orcid.org/0000-0001-5634-5559 2021. Analytic evaluation of the fractional moments for the quasi-stationary distribution of the shiryaev martingale on an interval. Communications in Statistics - Simulation and Computation 50 (9) , pp. 2705-2720. 10.1080/03610918.2019.1612433

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Abstract

We consider the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval [0,A] [0,A] with absorption at a fixed A > 0. We derive analytically a closed-form formula for the distribution’s fractional moment of an arbitrary given order s∈R; the formula is consistent with that previously found by Polunchenko and Pepelyshev for the case of s∈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→+∞; the limiting exponential distribution is the stationary distribution of the reciprocal of the Shiryaev diffusion.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Taylor & Francis
ISSN:	0361-0918
Date of First Compliant Deposit:	16 April 2019
Date of Acceptance:	18 April 2019
Last Modified:	23 Nov 2024 17:00
URI:	https://orca.cardiff.ac.uk/id/eprint/121826

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