Integrability and tail estimates for Gaussian rough differential equations
arXiv:1104.1813 · 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.
Published in at http://dx.doi.org/10.1214/12-AOP821 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
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- Fractal Dimensions of Rough Differential Equations Driven by Fractional Brownian Motions
- Smoothness of densities for path-dependent SDEs under Hörmander's condition
- Existence of densities for stochastic evolution equations driven by fractional Brownian motion
- A Stratonovich-Skorohod integral formula for Volterra Gaussian rough paths
- Small ball probabilities, metric entropy and Gaussian rough paths