关于Shiryaev-Roberts扩散的拟平稳分布的收敛速度

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

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引用次数: 2

摘要

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。

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

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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来源期刊

Sequential Analysis-Design Methods and Applications STATISTICS & PROBABILITY-

CiteScore

1.40

自引率

12.50%

发文量

期刊介绍： The purpose of Sequential Analysis is to contribute to theoretical and applied aspects of sequential methodologies in all areas of statistical science. Published papers highlight the development of new and important sequential approaches. Interdisciplinary articles that emphasize the methodology of practical value to applied researchers and statistical consultants are highly encouraged. Papers that cover contemporary areas of applications including animal abundance, bioequivalence, communication science, computer simulations, data mining, directional data, disease mapping, environmental sampling, genome, imaging, microarrays, networking, parallel processing, pest management, sonar detection, spatial statistics, tracking, and engineering are deemed especially important. Of particular value are expository review articles that critically synthesize broad-based statistical issues. Papers on case-studies are also considered. All papers are refereed.