Large deviations analysis of some recursive algorithms with state dependent noise (Q1113175)

The problem of proving large deviation-type theorems for \[ X^{\epsilon}_{n+1}=X_ n^{\epsilon}+\epsilon b(X_ n^{\epsilon},\xi_ n) \] where \(\xi_ n\) is a random process and \(X_ n^{\epsilon}\) is in \(R^ d\) is considered. The theorems are proved for the general case of stochastic processes with Lipschitz continuous sample paths. The assumptions are stated in terms of conditional distributions of time increments of the processes. Several examples are given.