Seminar

It is well known from the results of A.Zvonkin, A.Veretennikov, N.Krylov, A.Davie, F.Flandoli, J.Mattingly and other probabilists that ordinary differential equations (ODEs) regularize in the presence of noise. Even if an ODE is "very bad" and has no solutions (or has many solutions), then the addition of a random noise leads (almost surely) to a "nice" ODE with a unique solution.  We investigate the same phenomenon for a heat equation with a drift. We prove that for almost all trajectories of random white noise the perturbed heat equation has a unique solution (even if the original heat equation with a drift had many or no solutions).(Joint work with Leonid Mytnik.)