Strong well posedness of McKean–Vlasov stochastic differential equations with Hölder drift
By P. C. D. Raynal. Stochastic Processes and their Applications, 2015
107 citations recorded by the source corpus.
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.
Subfields: Finance, Modeling and Simulation, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/3fc740e5c48aa49cbc1292b01c795afaf11995d9
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Citations in the corpus
- Weak quantitative propagation of chaos via differential calculus on the space of measures (2019, unknown): “Article [14] considers the method of parametrix.”
- Mckean-Vlasov sdes with drifts discontinuous under wasserstein distance (2020, background): “Recently, the (weak and strong) well-posedness is studied in [3, 4, 6, 13, 17, 18, 20] for (1) with σt(x, γ) = σt(x) independent of the distribution variable γ, and with singular drift bt(x, γ).”