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Integrability and tail estimates for Gaussian rough differential equations

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JournalAnnals of Probability
DateE-pub ahead of print - 3 Jul 2013
DatePublished (current) - 20 Aug 2013
Issue number4
Volume41
Number of pages25
Pages (from-to)3026-3050
Early online date3/07/13
Original languageEnglish

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 parameterH > 1/4. We remark on the relevance of such estimates to a number of significant open problems.

    Research areas

  • Gaussian processes, Rough path analysis

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