Electronic Journal of Probability

On the small deviation problem for some iterated processes

Frank Aurzada and Mikhail Lifshits

Full-text: Open access

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

Permanent link to this document
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

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

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

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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