Laws of the iterated logarithm for a class of iterated processes

Erkan Nane

Statistics & Probability Letters, 2009, vol. 79, issue 16, 1744-1751

Abstract: Let X={X(t),t>=0} be a Brownian motion or a spectrally negative stable process of index 1 =0} be the hitting time of a stable subordinator of index 0 0. This establishes the lower bound in the law of the iterated logarithm which we could not prove with the techniques of our paper [Meerschaert, M.M., Nane, E., Xiao, Y.. 2008. Large deviations for local time fractional Brownian motion and applications. J. Math. Anal. Appl. 346, 432-445]. We also obtain exact small ball probability for X(E(t)) using ideas from Aurzada and Lifshits [Aurzada, F., Lifshits, M., On the small deviation problem for some iterated processes. preprint: arXiv:0806.2559].

Date: 2009
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