Integrability and tail estimates for Gaussian rough differential equations

• Autores: Thomas Cass, Christian Litterer, Terry J. Lyons
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 4, 2013, págs. 3026-3050
• Idioma: inglés
• DOI: 10.1214/12-AOP821
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• Resumen

  • 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.