I will discuss an importance sampling method for certain rare event
problems involving small noise diffusions. Standard Monte Carlo
schemes for these problems behave exponentially poorly in the small
noise limit. Previous work in rare event simulation has focused on
developing, in
specific situations,
estimators with optimal exponential variance decay rates. I will introduce
an estimator related to a
deterministic control problem that not only has an optimal variance decay
rate under certain conditions, but that can even have vanishingly small
statistical relative error in the small noise limit.
The method can be seen as the limit of a well known
zero variance importance sampling scheme for diffusions which
requires the solution of a second order partial differential
equation. I will also report on progress toward applying the algorithm
within the design of magnetic memory devices.
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