Robustness and Approximation of Escape Times and Large Deviations Estimates for Systems with Small Noise Effects,

Abstract

Abstract : For the purposes of estimating escape time from a given set, or other statistical properties of systems with small noise effects, it is generally assumed in applications that the system noise is white Gaussian. The Gaussian assumption greatly simplifies the computation, but is not adequate for many important classes of applications to control and communication theory. For example, when the noise is small, the mean escape time from a set can be quite sensitive to the underlying statistics even though in the study of the effects of the noise over any fixed finite time interval, the Gaussian approximation might be a good one. This paper is concerned with the sensitivity of these statistical quantities to the underlying statistical structure, when the noise effects are small, and also with the question of when the Gaussian assumption makes sense.