Large Deviations for a Class of Stochastic Semi-linear Partial Differential Equations

Leila Setayeshgar, Department of Mathematics & Computer Science, Providence College, USA

Standard approaches to large deviations analysis for stochastic partial differential equations (SPDEs) are often based on approximations. These approximations are mostly technical and often onerous to carry out. In 2008, Budhiraja, Dupuis and Maroulas, employed the weak convergence approach and showed that these approximations can be avoided for many infinite dimensional models. Large deviations analysis for such systems instead relied on demonstrating existence, uniqueness and tightness properties of certain perturbations of the original process. In this talk, we use the weak convergence approach, and establish the large deviation principle for the law of the solutions to a class of semi-linear SPDEs. Our family of semi-linear SPDEs contains, as special cases, both the stochastic Burgers' equation, and the stochastic reaction-diffusion equation.

Please direct all questions to the following contacts - Your question will be routed to get you an answer as quickly as possible.

• MSUStatSymposium2018@stt.msu.edu
• Michigan State University
  Department of Statistics and Probability
  Room C413 Wells Hall
  619 Red Cedar Road
  East Lansing, MI 48824