Date: 2014-01-10

Time: 15:30-16:30

Location: BURN 1205

Abstract:

In a seminal article in 1944, Itô introduced the stochastic integral with respect to the Brownian motion, which turned out to be one of the most fruitful ideas in mathematics in the 20th century. This lead to the development of stochastic analysis, a field which includes the study of stochastic partial differential equations (SPDEs). One of the approaches for the study of SPDEs was initiated by Walsh (1986) and relies on the concept of random-field solution for equations perturbed by a space-time white noise (or Brownian sheet). This concept allows us to investigate the dynamical changes in the probabilistic behavior of the solution, simultaneously in time and space. These developments will be reviewed in the first part of the talk. The second part of the talk will be dedicated to some recent advances in this area, related to the existence of a random-field solution for some classical SPDEs (like the stochastic heat equation) perturbed by a colored'' noise, which behaves in time like the fractional Brownian motion. When this solution exists, it exhibits a strong form of intermittency,’’ a property which was originally introduced in the physics literature for describing random fields whose values develop very large peaks. This talk is based on some recent joint work with Daniel Conus (Lehigh University).

Speaker

Raluca Balan is a professor at the University of Ottawa.