Strong well-posedness of McKean-Vlasov stochastic differential equation with Hölder driftReport as inadecuate




Strong well-posedness of McKean-Vlasov stochastic differential equation with Hölder drift - Download this document for free, or read online. Document in PDF available to download.

1 LAMA - Laboratoire de Mathématiques

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.





Author: Paul-Eric Chaudru de Raynal -

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



DOWNLOAD PDF




Related documents