Electronic Journal of Probability

On the small deviation problem for some iterated processes

Frank Aurzada and Mikhail Lifshits

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G18: Self-similar processes
Secondary: 60F99: None of the above, but in this section 60G12: General second-order processes 60G52: Stable processes

small deviations small ball problem iterated Brownian motion iterated fractional Brownian motion iterated process local time

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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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