Li, Kexian, Polunchenko, Aleksey and Pepelyshev, Andrey ![]() |
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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 |
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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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