Abstract
Large deviation theory is an asymptotic theory for stochastic systems far from their equilibrium, and is especially effective for the analysis of rare events. For this reason, large deviation theory has been recognized as a powerful tool in areas that treat stochastic phenomena. Also, in the area of nonlinear filtering, singular perturbation approaches have increasingly been used to break through the nonlinearity of stochastic systems. Large deviation theory gives a basis to the singular perturbations of stochastic systems. In this paper, we give a tutorial explanation of the basis of large deviation theory and present its application to nonlinear filtering, including our application to adaptive state estimation.
