The Annals of Probability

Integrability and tail estimates for Gaussian rough differential equations

Thomas Cass, Christian Litterer, and Terry Lyons

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Abstract

We derive explicit tail-estimates for the Jacobian of the solution flow for stochastic differential equations driven by Gaussian rough paths. In particular, we deduce that the Jacobian has finite moments of all order for a wide class of Gaussian process including fractional Brownian motion with Hurst parameter $H>1/4$. We remark on the relevance of such estimates to a number of significant open problems.

Article information

Source
Ann. Probab., Volume 41, Number 4 (2013), 3026-3050.

Dates
First available in Project Euclid: 3 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.aop/1372859772

Digital Object Identifier
doi:10.1214/12-AOP821

Mathematical Reviews number (MathSciNet)
MR3112937

Zentralblatt MATH identifier
1278.60091

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60G15: Gaussian processes

Keywords
Rough path analysis Gaussian processes

Citation

Cass, Thomas; Litterer, Christian; Lyons, Terry. Integrability and tail estimates for Gaussian rough differential equations. Ann. Probab. 41 (2013), no. 4, 3026--3050. doi:10.1214/12-AOP821. https://projecteuclid.org/euclid.aop/1372859772


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References

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