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 parameterH > 1/4. We remark on the relevance of such estimates to a number of significant open problems.
|Number of pages||25|
|Journal||Annals of Probability|
|Early online date||3 Jul 2013|
|Publication status||Published - 20 Aug 2013|
- Gaussian processes
- Rough path analysis