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math.PR2022
Functional law of large numbers and central limit theorem for slow-fast McKean-Vlasov equations
Yun Li, Longjie Xie
In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first e…
math.PR2016
Singular SDEs with critical non-local and non-symmetric Lévy type generator
Longjie Xie
In this work, by using Levi's parametrix method we first construct the fundamental solution of the critical non-local operator perturbed by gradient. Then, we use the obtained esti…