## Electronic Journal of Probability

### On the small deviation problem for some iterated processes

#### 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, Electron. J. Probab. 11 (2006), no. 18, 434--459.

#### Article information

Source
Electron. J. Probab., Volume 14 (2009), paper no. 68, 1992-2010.

Dates
Accepted: 28 September 2009
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464819529

Digital Object Identifier
doi:10.1214/EJP.v14-689

Mathematical Reviews number (MathSciNet)
MR2550290

Zentralblatt MATH identifier
1190.60016

Rights

#### Citation

Aurzada, Frank; Lifshits, Mikhail. On the small deviation problem for some iterated processes. Electron. J. Probab. 14 (2009), paper no. 68, 1992--2010. doi:10.1214/EJP.v14-689. https://projecteuclid.org/euclid.ejp/1464819529

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