Stochastic control and large deviations

Abstract

Large deviations theory is concerned with asymptotic estimates of probabilities of rare events associated with stochastic processes. A stochastic control approach to large deviations is outlined. Both problems of small random perturbations and large deviations from ergodicity are considered. For large deviations of Markov diffusion processes, PDE — viscosity solution methods are mentioned. Another stochastic control formulation, applicable to a broad range of large deviations problems is due to Dupuis and Ellis. This approach reduces many aspects of large deviations to the theory of weak convergence of probability measures.