Special Session 11: Stochastic Partial Differential Equations

The Leibenson process as a strong solution to its associated McKean--Vlasov SDE
Sebastian Grube
Bielefeld University
Germany
Co-Author(s):    Viorel Barbu, Marco Rehmeier, Michael Roeckner
Abstract:
This talk continues the presentation by Marco Rehmeier. The Leibenson process, a nonlinear Markov process, is constructed from the path laws of probabilistically weak solutions to a class of McKean--Vlasov SDEs associated to the Leibenson equation. Despite the low regularity of the coefficients of these highly degenerate McKean--Vlasov SDEs, we can show that the weak solutions constituting the Leibenson process are, in fact, strong solutions. As a special case, we show that the $p$-Brownian motion is a strong solution to its associated McKean--Vlasov SDE.