Year: 2013
Type: article
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.
Source: The Annals of Probability
DOI: 10.1214/12-aop821
Authors: Thomas Cass, Christian Litterer, Terry Lyons
Institutions: University of Oxford, Imperial College London
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: bronze
Awards: G2229479377, Increasing the efficiency of numerical methods for estimating the state of a partially observed system. High order methods for solving parabolic PDEs, Rough path theory, differential equations and stochastic analysis, G5224691083, G7326578543, Rough path analysis and non-linear stochastic systems
OpenAlex ID: W2093600994