On the exact constants in one-sided maximal inequalities for Bessel processes

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Sequential Analysis-Design Methods and Applications Pub Date : 2023-01-02 DOI:10.1080/07474946.2022.2150778

C. Makasu

引用次数: 1

Abstract

Abstract In this paper, we establish a one-sided maximal moment inequality with exact constants for Bessel processes. As a consequence, we obtain an exact constant in the Burkholder-Gundy inequality. The proof of our main result is based on a pure optimal stopping problem of the running maximum process for a Bessel process. The present results extend and complement a number of related results previously known in the literature.

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关于贝塞尔过程单侧极大不等式的精确常数

摘要本文建立了贝塞尔过程具有精确常数的单侧极大矩不等式。因此，我们在Burkholder-Gundy不等式中得到了一个精确常数。我们的主要结果的证明是基于一个贝塞尔进程运行最大进程的纯最优停止问题。目前的结果扩展和补充了文献中先前已知的一些相关结果。

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

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.