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On transient Bessel processes and planar Brownian motion reflected at their future infima

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  • Shi, Z.

Abstract

Let R be a transient Bessel process and let J(t) = infu>=t R(u) be its future infimum process. The main result of this paper is an integral test characterizing the upper functions of R - J, which turn out to be quite different from those of R. The test implies in particular an iterated logarithm law recently obtained by Khoshnevisan et al. (1994), and also solves the problem of characterizing the large gaps between the past supremum and future infimum of R. The corresponding local question for a planar Wiener process is studied.

Suggested Citation

  • Shi, Z., 1995. "On transient Bessel processes and planar Brownian motion reflected at their future infima," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 87-102, November.
    • Handle: RePEc:eee:spapps:v:60:y:1995:i:1:p:87-102
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    Cited by:

    1. Shi, Zhan, 1996. "Brownian motion normalized by maximum local time," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 217-231, December.
    2. Endre Csáki & Antónia Földes & Pál Révész, 2009. "Transient Nearest Neighbor Random Walk and Bessel Process," Journal of Theoretical Probability, Springer, vol. 22(4), pages 992-1009, December.

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