Small ball probabilities for a class of time-changed self-similar processes

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• 作者：Kei Kobayashi ; ^{kkobayas@utk.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60F99 ; 60G18 ; 60G51
• 刊名：Statistics & Probability Letters
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：110
• 期：Complete
• 页码：155-161
• 全文大小：384 K

文摘

This paper establishes small ball probabilities for a class of time-changed processes X∘E$X\circ E$, where X$X$ is a self-similar process and 85827dd2513" title="Click to view the MathML source">E$E$ is an independent continuous process, each with a certain small ball probability. In particular, examples of the outer process X$X$ and the time change 85827dd2513" title="Click to view the MathML source">E$E$ include an iterated fractional Brownian motion and the inverse of a general subordinator with infinite Lévy measure, respectively. The small ball probabilities of such time-changed processes show power law decay, and the rate of decay does not depend on the small deviation order of the outer process X$X$, but on the self-similarity index of X$X$.