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A remark on the multiparameter law of the iterated logarithm

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  • Lacey, Michael T.

Abstract

Let B(s, t), s, t > 0, be a Brownian sheet. In contrast to the usual law of the iterated logarithm for B, we prove that There is no analog of this limit for the Brownian motion. Generalizations of this are also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:32:y:1989:i:2:p:355-367
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    Cited by:

    1. Lin, Zheng Yan & Choi, Yong-Kab, 1999. "Some limit theorems for fractional Lévy Brownian fields," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 229-244, August.
    2. 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.
    3. 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.

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