Large Deviations for Diffusions Depending on Small Parameters: A Stochastic Control Method.
BROWN UNIV PROVIDENCE R I LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS
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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
- Statistics and Probability