Mapping spatial persistent large deviations of nonequilibrium surface growth processes onto the temporal persistent large deviations of stochastic random walk processes

Large Deviations for Stochastic Processes

The purpose of these lectures is to introduce you to the basics of large deviation theory. The emphasis will be on the use of compactness ideas (more extensive results are in Puhalskii [13]). Other approaches to large deviation theory are considered in Dembo and Zeitouni [3], den Hollander [4], Deuschel and Stroock [6], Dupuis and Ellis [7], Freidlin and Wentzell [9], Kallenberg [12], Shwartz a...

Large Deviations for Stochastic Processes

The notes are devoted to results on large deviations for sequences of Markov processes following closely the book by Feng and Kurtz ([FK06]). We outline how convergence of Fleming’s nonlinear semigroups (logarithmically transformed nonlinear semigroups) implies large deviation principles analogous to the use of convergence of linear semigroups in weak convergence. The latter method is based on ...

Large Deviations for Stochastic Processes

The theory of large deviations deals with the estimation of small probabilities, particularly those that are exponentially small in some natural parameter. The general goal is to identify the constant in the exponent that dictates the exponential rate of decay. In many situations the constant can be “explicitly” calculated and turns out often to be characterized by a variational formula. It is ...

Nonequilibrium Markov Processes Conditioned on Large Deviations

Large Deviations for Random Walk in Random