Applied Maths Seminar: Aryasova -- Limit theorems for sticky SDEs with local times and applications to stochastic homogenization

Olga Aryasova (University of Jena) will be visiting us next week and will give a talk on
Tuesday 24 March at 1pm in the AGR (note unusual date, time, location).  

Title: Limit theorems for sticky SDEs with local times and applications to stochastic
homogenization 

Abstract: We establish a general convergence theorem for solutions of multivariate
stochastic differential equations with countably many singular terms expressed as
integrals with respect to local times.  The processes under consideration describe
diffusions in the presence of semipermeable hyperplane interfaces.  These interfaces may
become sticky after applying a random time change that depends on the amount of local
time accumulated on each interface.  We show that, as the distance between the
interfaces tends to zero, the local-time terms converge to a limiting homogenized drift
term.  When the interfaces are sticky, the limiting diffusion also decelerates, meaning
that its diffusion coefficient is effectively reduced.  Such limit theorems illustrate a
form of stochastic homogenization for diffusions evolving in a heterogeneous medium
interleaved with semipermeable, sticky interfaces.