On the Small Deviation Problem for Some Iterated Processes

Details On the Small Deviation Problem for Some Iterated Processes On the Small Deviation Problem for Some Iterated Processes

2008-06-16

arxiv.org/abs/0806.2559v1

Electron. J. Probab., 2009, 14, no. 68, 1992--2010

Mathematics

Probability

Preprint, 21p

Scientific paper

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 $\alpha$-time Brownian motion, Electron. J. Probab. 11 (2006), no. 18, 434--459.

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