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2009 On the small deviation problem for some iterated processes
Frank Aurzada, Mikhail Lifshits
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Electron. J. Probab. 14: 1992-2010 (2009). DOI: 10.1214/EJP.v14-689


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.


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Frank Aurzada. Mikhail Lifshits. "On the small deviation problem for some iterated processes." Electron. J. Probab. 14 1992 - 2010, 2009.


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

zbMATH: 1190.60016
MathSciNet: MR2550290
Digital Object Identifier: 10.1214/EJP.v14-689

Primary: 60G18
Secondary: 60F99 , 60G12 , 60G52

Keywords: iterated Brownian motion , iterated fractional Brownian motion , iterated process , Local time , small ball problem , Small deviations

Vol.14 • 2009
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