# Strong well-posedness of McKean-Vlasov stochastic differential equation with HÃ¶lder drift

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1 LAMA - Laboratoire de MathÃ©matiques

Abstract : In this paper, we prove pathwise uniqueness for stochastic systems of McKean-Vlasov type with singular drift, even in the measure argument, and uniformly non-degenerate Lipschitz diffusion matrix. Our proof is based on Zvonkin-s transformation \cite{zvonkin transformation 1974} and so on the regularization properties of the associated PDE, which is stated on the space $0,T\times \R^d\times \mathcal{P} 2\R^d$, where $T$ is a positive number, $d$ denotes the dimension equation and $\mathcal{P} 2\R^d$ is the space of probability measures on $\R^d$ with finite second order moment. Especially, a smoothing effect in the measure direction is exhibited. Our approach is based on a parametrix expansion of the transition density of the McKean-Vlasov process.

Autor: Paul-Eric Chaudru de Raynal -

Fuente: https://hal.archives-ouvertes.fr/

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