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

Kexuan Li, Aleksey S. Polunchenko, Andrey Pepelyshev

Результат исследований: Научные публикации в периодических изданияхстатья

Аннотация

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 arbitrary given order s Є R the formula is consistent with that previously found by Polunchenko and Pepelyshev for the case of s Є 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.

Язык оригиналаанглийский
ЖурналCommunications in Statistics: Simulation and Computation
Ранняя дата в режиме онлайн6 июн 2019
DOI
СостояниеЭлектронная публикация перед печатью - 6 июн 2019

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Предметные области Scopus

  • Теория вероятности и статистика
  • Моделирование и симуляция

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