Remark on maximal inequalities for Bessel processes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:482

Article

Makasu, Cloud¹ 

[1] Univ Western Cape, Dept Maths & Appl Maths, Private Bag X17, ZA-7535 Cape Town, South Africa

关键词: Bessel processes;    Maximal inequalities;    Optimal stopping problem;    Reverse Young inequality;   

DOI  :  10.1016/j.jmaa.2019.123531

来源: Elsevier

【 摘 要 】

For a Bessel process X = (X-t)(t >= 0) with dimension alpha > 0 starting at zero, a result of Dubins, Shepp and Shiryaev (1993) states that there exists a constant gamma(alpha) depending only on alpha such that E ((max)(0 <= t <=tau) X-t) <=gamma(alpha) root E(tau) for any stopping time tau of X. In this paper, we give an explicit form of the constant gamma(alpha) in the case 0 < alpha <= 1. The present result complements the known case when alpha > 1 treated in Graversen and Peskir (1998). (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free