Large Deviations for Diffusions Depending on Small Parameters: A Stochastic Control Method.

摘要

This paper considers stochastic differential equations depending on a small parameter epsilon, which enters as a coefficient in the noise term of the equation. The Ventcel-Freidlin estimates give an asymptotic formula as epsilon approaches 0 for the probability that a solution trajectory hits a given compact set B during a given time interval. A stochastic control method to obtain such estimates is outlined. Detailed proofs are given elsewhere. (Author)