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
Title: Computability of martingale convergence
In both probability theory and computability theory, an important theme is “information”, and an important tool for studying information is a “martingale”. Informally, a martingale is a betting strategy. More formally, it is a sequence of random variables $M_n$ such that $E[M_{n+1} \mid M_n] = M_n$. There are many well known convergence results for martingales. In this talk I will discuss two methods for investigating the computability of martingale convergence. First I will give general conditions for when the rate of convergence of a martingale is computable. Second, I will characterize the points for which computable martingales converge. Such questions are interesting because they provide a bridge between the practical applications of probability theory on one hand and its nonconstructive set theoretic foundations on the other. This also ties in closely to the logical topics of algorithmic randomness and constructive/computable mathematics.
The Lovasz local lemma and its application in logic / theoretical computer science
Topic: Nondeterministic finite state complexity