A Functional LIL for Stochastic Integrals and the L¨¦vy Area Process

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• 作者：James Kuelbs and Wenbo Li
• 关键词：Functional LIL ; L&eacute ; vys area process ; small ball probabilities
• 刊名：Journal of Theoretical Probability
• 出版年：2005
• 出版时间：2005
• 年：2005
• 卷：18
• 期：2
• 页码：261-290
• 全文大小：241 KB

文摘

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 Lévys 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.