On large deviations theory and asymptotically efficient Monte Carlo estimation

It is shown how large-deviations theory can be applied to construct an asymptotically efficient simulation distribution for Monte Carlo simulation using the importance sampling technique. A sufficient and necessary condition is given for the asymptotic efficiency of the candidate simulation distributions. This is done in the multidimensional setting that is required by many practical simulation problems. The result obtained is applied primarily in two areas. First, the generalization of previous work dealing with functionals of Markov chains is discussed. A second area of application is the simulation of nonlinear systems with Gaussian inputs. As an example of a system with Gaussian inputs, the simulation of a digital communication channel with nonlinear ISI (intersymbol interference) characteristic of satellite data links is considered. In the case of linear ISI, the asymptotically efficient exponentially twisted distribution turns out to agree with a method previously proposed by D. Lu and K. Yao (1988). The large-deviations point of view provides some useful insight on how to extent the Lu and Yao method to nonlinear channels.<
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