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Importance sampling for McKean-Vlasov SDEs. (arXiv:1803.09320v2 [math.PR] UPDATED)
来源于:arXiv
This paper deals with the Monte-Carlo methods for evaluating expectations of
functionals of solutions to McKean-Vlasov Stochastic Differential Equations
(MV-SDE) with drifts of super-linear growth. We assume that the MV-SDE is
approximated in the standard manner by means of an interacting particle system
and propose two importance sampling (IS) techniques to reduce the variance of
the resulting Monte Carlo estimator. In the \emph{complete measure change}
approach, the IS measure change is applied simultaneously in the coefficients
and in the expectation to be evaluated. In the \emph{decoupling} approach we
first estimate the law of the solution in a first set of simulations without
measure change and then perform a second set of simulations under the
importance sampling measure using the approximate solution law computed in the
first step.
For both approaches, we use large deviations techniques to identify an
optimisation problem for the candidate measure change. The decoupling approac 查看全文>>