Title: Stochastic processes associated with dispersion across sharp
interfaces

Abstract: Dispersion in highly heterogeneous environment, as characterized
by abrupt changes (discontinuities) in the diffusion coefficient (such
discontinuous points are called interfaces), can be studied via the
identification of the associated stochastic process. The challenge here is
connecting the PDE that governs such dispersion to a stochastic process.
One cannot apply the classical Ito formula in this case as the domain of
the infinitesimal generator of such stochastic processes are not C^2. In
this talk I’ll give few examples of dispersion in heterogeneous
environment and explain how to identify the associated stochastic
processes. Ill also discuss effect of interfaces on breakthrough curves
(first passage times) and occupation times of the process.

Thilanka Appuhamillage