Remark on maximal inequalities for Bessel processes

Remark on maximal inequalities for Bessel processes

For a Bessel process X=(Xt)t≥0 with dimension α>0 starting at zero, a result of Dubins, Shepp and Shiryaev (1993) states that there exists a constant γ(α) depending only on α such thatE(max0≤t≤τ⁡Xt)≤γ(α)E(τ) for any stopping time τ of X. In this paper, we give an explicit form of the constant γ(α...

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Veröffentlicht in:Journal of mathematical analysis and applications 2020-02, Vol.482 (1), p.123531, Article 123531
1. Verfasser: Makasu, Cloud
Format: Artikel
Sprache:eng
Schlagworte:
Bessel processes
Maximal inequalities
Optimal stopping problem
Reverse Young inequality
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Zusammenfassung:For a Bessel process X=(Xt)t≥0 with dimension α>0 starting at zero, a result of Dubins, Shepp and Shiryaev (1993) states that there exists a constant γ(α) depending only on α such thatE(max0≤t≤τ⁡Xt)≤γ(α)E(τ) for any stopping time τ of X. In this paper, we give an explicit form of the constant γ(α) in the case 01 treated in Graversen and Peskir (1998).
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.123531