Sobolev differentiable flows of SDEs with local Sobolev and super-linear growth coefficients

• Longjie Xie ^[1] ; Xicheng Zhang ^[1]
  1. [1] Wuhan University

     Wuhan University

     China

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 6, 2016, págs. 3661-3687
• Idioma: inglés
• DOI: 10.1214/15-aop1057
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• Resumen

  • By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility to the associated diffusion semigroup.