Integrability and tail estimates for Gaussian rough differential equations

Citation
Cass, Thomas et al., Integrability and tail estimates for Gaussian rough differential equations, Annals of probability , 41(4), 2013, pp. 3026-3050
Journal title
ISSN journal
00911798
Volume
41
Issue
4
Year of publication
2013
Pages
3026 - 3050
Database
ACNP
SICI code
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.