DMS Colloquium: Erkan Nane

Speaker: Erkan Nane

Title: Stochastic Models for Fractional Dynamics

Abstract: My research interests lie in the interface of probability and  various areas of analysis, particularly  harmonic analysis, partial differential equations, geometry and potential theory. Recently, much of my research has been focused on  fundamental properties of stochastic fractional equations, and  time-changed stochastic processes that arise as scaling limits of continuous time random walks.  These novel processes are interesting on their own, and they have  recently  been applied to model various phenomena in a wide range of scientific areas including physics, telecommunications, turbulence, image processing, biology, bioengineering, hydrology, geophysics and finance.

In this talk I will give highlights of  my research during the past 5 years.   In particular, I will review my most recent work on
(i)  continuous time random walk limits;
(ii) heat type Cauchy problems with  fractional time derivatives;  and
(iii) stochastic fractional equations.