On the Small Deviation Problem for Some Iterated Processes

Frank Aurzada; Mikhail Lifshits

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arXiv · 0806.2559

On the Small Deviation Problem for Some Iterated Processes

Frank Aurzada·Mikhail Lifshits

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Abstract

We derive general results on the small deviation behavior for some classes of iterated processes. This allows us, in particular, to calculate the rate of the small deviations for $n$-iterated Brownian motions and, more generally, for the iteration of $n$ fractional Brownian motions. We also give a new and correct proof of some results in E. Nane, Laws of the iterated logarithm for $α$-time Brownian motion, Electron. J. Probab. 11 (2006), no. 18, 434--459.

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Frank Aurzada, Mikhail Lifshits. 2008-06-16. On the Small Deviation Problem for Some Iterated Processes. https://arxiv.org/abs/0806.2559

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