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Some liminf results for two-parameter processes

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  • Csáki, Endre
  • Shi, Zhan

Abstract

We obtain some liminf limits for the Wiener sheet. The approach relies on a careful analysis of the lower tail of the Ornstein-Uhlenbeck process. Our results can be applied to normalized Kiefer and empirical processes. In particular, they yield a satisfying answer to Hirsch's problem for the uniform empirical distribution function.

Suggested Citation

  • Csáki, Endre & Shi, Zhan, 1998. "Some liminf results for two-parameter processes," Stochastic Processes and their Applications, Elsevier, vol. 78(1), pages 27-46, October.
    • Handle: RePEc:eee:spapps:v:78:y:1998:i:1:p:27-46
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    References listed on IDEAS

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    1. Zhang, Li-Xin, 1996. "Two different kinds of liminfs on the LIL for two-parameter Wiener processes," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 175-188, November.
    2. Lacey, Michael T., 1989. "A remark on the multiparameter law of the iterated logarithm," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 355-367, August.
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    Cited by:

    1. Endre Csáki & Yueyun Hu, 2004. "On the Ranked Excursion Heights of a Kiefer Process," Journal of Theoretical Probability, Springer, vol. 17(1), pages 145-163, January.

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