Joint USYD-UNSW Seminar on Stochastic PDEs: Michael Roeckner (Bielefeld University) -- Nonlinear Markov processes in the sense of McKean

Zoom link: https://uni-sydney.zoom.us/j/88112068402?from=addon 

In the talk we shall discuss nonlinear Markov processes in the sense of McKean 
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 
coefficients are only assumed to be measurable in their measure variable, so that they
may depend on derivatives of any order of the time-marginal densities of solutions.  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.