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

Abstract

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 of the associated diffusion semigroup.

to appear in Annals of Probability

References in corpus (3)

• Well-posedness of the transport equation by stochastic perturbation
• Noise Prevents Singularities in Linear Transport Equations
• Degenerate SDE with Hölder-Dini Drift and Non-Lipschitz Noise Coefficient

Cited by in corpus (1)

• Regime-switching diffusion processes: strong solutions and strong Feller property