Variance Rate Theory of Conditional Importance Sampling Estimators

Abstract

We consider again our usual framework: for every integer n, let Z _{p ,n} be a random variable taking values in some complete separable metric space S _n . Let P _n be the probability measure induced by Z _p,n on S _n . We suppose that for each random variable Z _p,n we have access to some information about it contained in an information random variable Z _pi,n taking values in some other probability space I _n . Let P _i,n denote the probability measure induced by Z _pi,n on I _n . Let f _n be an R ^d-valued measurable function on the space S _n ; that is, f _n : S _n → R _d , and we suppose we are interested in ρ _n = P(f _n (Z _p,n ) Є nE), for some Borel set E ⊂ R ^d.

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