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A Functional LIL for Stochastic Integrals and the Lévy Area Process

Author

Listed:
  • James Kuelbs

    (University of Wisconsin)

  • Wenbo Li

    (University of Delaware)

Abstract

A functional law of the iterated logarithm is obtained for processes given by certain stochastic integrals. This extends earlier results by Shi(12) and Rémillard(10) who established analogues of the classical limit results of Chung(4) for a variety of processes, including Lévy’s stochastic area process. The functional aspects of our results are motivated by a paper of Wichura(13) on Brownian motion. Proofs depend on small ball probability estimates, and yield the small ball probabilities of the weighted sup-norm for the processes given by these stochastic integrals.

Suggested Citation

  • James Kuelbs & Wenbo Li, 2005. "A Functional LIL for Stochastic Integrals and the Lévy Area Process," Journal of Theoretical Probability, Springer, vol. 18(2), pages 261-290, April.
    • Handle: RePEc:spr:jotpro:v:18:y:2005:i:2:d:10.1007_s10959-003-2604-9
    DOI: 10.1007/s10959-003-2604-9
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