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Quadratic transportation inequalities for SDEs with measurable drift

Abstract : 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.
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Submitted on : Friday, March 6, 2020 - 9:09:13 PM
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Khaled Bahlali, Soufiane Mouchtabih, Ludovic Tangpi. Quadratic transportation inequalities for SDEs with measurable drift. Proceedings of the American Mathematical Society, American Mathematical Society, 2021, ⟨10.1090/proc/15477⟩. ⟨hal-02501467⟩



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