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math.PR2020
Averaging principle and normal deviations for multi-scale stochastic hyperbolic-parabolic equations
Michael Röckner, Longjie Xie, Li Yang
We study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are est…
math.PR2020★ 48 cited
Averaging principle and normal deviations for multiscale stochastic systems
Michael Röckner, Longjie Xie
We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization…
math.AP2020
Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations
Viorel Barbu, Michael Röckner
One proves the existence and uniqueness of a generalized (mild) solution for the nonlinear Fokker-Planck equation (FPE) \begin{align*} &u_t-Δ(β(u))+{\mathrm{ div}}(D(x)b(u)u)=0, \q…