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A ratio inequality for Bessel processes

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  • Yan, Litan
  • Zhu, Bei

Abstract

Let Z=(Zt)t[greater-or-equal, slanted]0 be a Bessel process of dimension [delta]>0 starting at zero. In this paper we show that the inequalitieshold for all 0 [phi](x) is a positive continuous function on [0,[infinity]) satisfying [lambda]1x[less-than-or-equals, slant][phi](x)[less-than-or-equals, slant][lambda]2xe[lambda]3x for three constants [lambda]1,[lambda]2,[lambda]3>0.

Suggested Citation

  • Yan, Litan & Zhu, Bei, 2004. "A ratio inequality for Bessel processes," Statistics & Probability Letters, Elsevier, vol. 66(1), pages 35-44, January.
    • Handle: RePEc:eee:stapro:v:66:y:2004:i:1:p:35-44
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    References listed on IDEAS

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    1. Pedersen, Jesper Lund, 2000. "Best Bounds in Doob's Maximal Inequality for Bessel Processes," Journal of Multivariate Analysis, Elsevier, vol. 75(1), pages 36-46, October.
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    Cited by:

    1. Chen Jia, 2019. "Sharp Moderate Maximal Inequalities for Upward Skip-Free Markov Chains," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1382-1398, September.

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