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July 2013 Integrability and tail estimates for Gaussian rough differential equations
Thomas Cass, Christian Litterer, Terry Lyons
Ann. Probab. 41(4): 3026-3050 (July 2013). DOI: 10.1214/12-AOP821

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.

Citation

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Thomas Cass. Christian Litterer. Terry Lyons. "Integrability and tail estimates for Gaussian rough differential equations." Ann. Probab. 41 (4) 3026 - 3050, July 2013. https://doi.org/10.1214/12-AOP821

Information

Published: July 2013
First available in Project Euclid: 3 July 2013

zbMATH: 1278.60091
MathSciNet: MR3112937
Digital Object Identifier: 10.1214/12-AOP821

Subjects:
Primary: 60H10
Secondary: 60G15

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 4 • July 2013
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