Back to Departmental Colloquium: Spring 2001
Departmental Colloquium
Date: Thursday, Feb 1, 2001
Time: 4:15PM
Location: JWB 335
Hassan Allouba
Indiana
Title |
Change of measure and SDDEs: Two approaches for stochastic PDEs and their applications |
Abstract |
Stochastic PDEs (SPDEs) form one of the hottest and most difficult fields in Probability theory and its interactions with PDEs and Stochastic Analysis. In this talk, I will describe two approaches which are effective in the study of existence, uniqueness, as well as qualitative behavior questions for SPDEs: Change of measure and SDDEs. The change of measure theorem generalizes the well known Girsanov theorem in the one parameter setting to that of SPDEs. This theorem takes on an added significance in the SPDEs setting, for it applies well to different types of equations and allows us, among other things, to transfer hard results from simpler to more complex SPDEs. I will give examples of applications to a class of equations containing the stochastic Allen-Cahn and others. The Stochastic Differential Difference Equations (SDDEs) approach starts by discretizing space in the corresponding SPDEs and then looking at limits as the spatial lattice size goes to zero. This approach has several advantages over the usual direct one. In addition to its numerical flavor, it provides for rich interplay between random walks and SPDEs, and allows us to prove otherwise hard results for these equations. It also gives us an interesting and “natural” class of solutions to SPDEs. Time permitting, I will discuss new applications to a class of Burgers-related stochastic equations. |
Probability
Mathematical Biology
Differential Equations