In the talk we shall discuss nonlinear Markov processes in the sense of McKean’s seminal work in PNAS 1966. In particular, we shall present a general new technique how to show that a family of probability measures on cadlag paths, given by the path laws of solutions to a McKean-Vlasov type SDE, form a nonlinear Markov process. The SDE’s coefficients are only assumed to be measurable in their measure variable, so that they may depend on derivatives of any order of the solutions’ time-marginal densities. In particular, the p-Brownian motion associated to the parabolic p-Laplace equation turns out to be a nonlinear Markov process in the sense of McKean. Further examples are related to the generalized (fractional) porous media equation, the Burgers and the 2D vorticity Navier-Stokes equation.
Joint work with Marco Rehmeier
Nonlinear Markov processes in the sense of McKean
.pdf [350Kb]
