REGULARIZATION BY STOCHASTIC DRIFT

Paul-Eric Chaudru de Raynal (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

We here prove pathwise (strong) uniqueness for degenerate systems with Hölder drift, for Hölder exponent larger than the critical value $c_c=2/3$. This work extends the one by Veretennikov, Krylov and Röckner and Flandoli from non-degenerate to degenerate cases. In comparison with, the non trivial value for $c_c$ is here the price to pay to balance the degeneracy of the noise. The main tool for proving strong solvability relies on regularization property of the associated PDE, which is degenerated in the current framework.

Keywords: Kolmogorov operator; Strong uniqueness; Hölder drift; Degeneracy; Stochastic Differential Equation

Domains: Probability [math.PR]

Paul-Eric Chaudru de Raynal. REGULARIZATION BY STOCHASTIC DRIFT. 2012. ⟨hal-00702532v1⟩