Integrability and tail estimates for Gaussian rough differential equations

Thomas Cass*, Christian Litterer, Terry Lyons

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)3026-3050
Number of pages25
JournalAnnals of Probability
Issue number4
Early online date3 Jul 2013
Publication statusPublished - 20 Aug 2013


  • Gaussian processes
  • Rough path analysis

Cite this