Quadratic transportation inequalities for SDEs with measurable drift

Khaled Bahlali (1) , Soufiane Mouchtabih , Ludovic Tangpi

1 IMATH - Institut de Mathématiques de Toulon - EA 2134

Let X be the solution of the multidimensional stochastic differential equation dX(t) = b(t, X(t)) dt + sigma(t, X(t)) dW(t)\, with X(0)=x where W is a standard Brownian motion. We show that when b is measurable and sigma is in an appropriate Sobolev space, the law of X satisfies a uniform quadratic transportation inequality.

Keywords: Quadratic transportation inequality; Stochastic differential equations; singular drifts; Sobolev regularity

Domains: Probability [math.PR]

Khaled Bahlali, Soufiane Mouchtabih, Ludovic Tangpi. Quadratic transportation inequalities for SDEs with measurable drift. Proceedings of the American Mathematical Society, 2021, ⟨10.1090/proc/15477⟩. ⟨hal-02501467⟩