On the convergence rate of the quasi- to stationary distribution for the Shiryaev-Roberts diffusion

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Sequential Analysis-Design Methods and Applications Pub Date : 2019-07-05 DOI:10.1080/07474946.2020.1766926

Kexuan Li, Aleksey S. Polunchenko

引用次数: 2

Abstract

Abstract For the classical Shiryaev-Roberts martingale diffusion considered on the interval where A > 0 is a given absorbing boundary, it is shown that the rate of convergence of the diffusion’s quasi-stationary cumulative distribution function (c.d.f.), to its stationary c.d.f., H(x), as is no worse than uniformly in The result is established explicitly by constructing new tight lower- and upper-bounds for using certain latest monotonicity properties of the modified Bessel K function involved in the exact closed-form formula for recently obtained by Polunchenko (2017b).

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关于Shiryaev-Roberts扩散的拟平稳分布的收敛速度

关于A区间上的经典Shiryaev-Roberts鞅扩散 > 0是一个给定的吸收边界，证明了扩散的拟平稳累积分布函数（c.d.f.）对其平稳c.d.f.，H（x）的收敛速度，通过使用Polunchenko（2017b）最近获得的精确闭合形式公式中涉及的修正贝塞尔K函数的某些最新单调性性质，构造新的紧下界和上界，明确地建立了结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Sequential Analysis-Design Methods and Applications STATISTICS & PROBABILITY-

CiteScore

1.40

自引率

12.50%

发文量

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