Mathematics – Probability
Scientific paper
2012-02-27
Mathematics
Probability
Scientific paper
In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and fast motion with small noise in the slow component. We assume periodicity with respect to the fast component. Depending on the interaction of the fast scale with the smallness of the noise, we get different behavior. We examine how one range of interaction differs from the other one both for the large deviations and for the importance sampling. We use the large deviations results to identify asymptotically optimal importance sampling schemes in each case. Standard Monte Carlo schemes perform poorly in the small noise limit. In the presence of multiscale aspects one faces additional difficulties and straightforward adaptation of importance sampling schemes for standard small noise diffusions will not produce efficient schemes. It turns out that one has to consider the so called cell problem from the homogenization theory for Hamilton-Jacobi-Bellman equations in order to guarantee asymptotic optimality. We use stochastic control arguments.
No associations
LandOfFree
Large Deviations and Importance Sampling for Systems of Slow-Fast Motion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Large Deviations and Importance Sampling for Systems of Slow-Fast Motion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Large Deviations and Importance Sampling for Systems of Slow-Fast Motion will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-263821