Speaker:

Jin Feng

Title:

Large deviation and variational problems

Abstract:

Large deviation asymptotic is closely related to variational problems and convergence. Such connection is what is behind many physical applications such as rigorous treatment of equilibrium thermodynamic formalism by David Ruelle, among others.

In the non-equilibrium case, one turns attention to stochastic processes. Inclusion of a time variable in dynamics allows us to formulate the variational connection at infinitesimal level. I will describe a recent attempt to connect large deviation for Markov processes with Hamilton-Jacobi equations. Examples ranging from Freidlin-Wentzell theory, Donsker-Varadhan theory, Dawson-Gartner theory (an infinite dimensional version of Freidlin-Wentzell) will be illustrated. In addition to applications, I hope to have time demonstrate that, such probabilistic connection can be useful in discovering ways of proving hard analysis theorem regarding viscosity solution for HJB equation in infinite dimensions.

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