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This paper briefly reviews the regenerative method for steady-state simulation, and then shows how regenerative structure can be used computationally to develop new estimators for the spectral density, moments of hitting times, and both discounted and average reward value functions. All our estimators typically exhibit the Monte Carlo method's usual “square root” convergence rate. This is in contrast...
Many Monte Carlo computations involve computing quantities that can be expressed as g(EX), where g is nonlinear and smooth, and X is an easily simulatable random variable. The nonlinearity of g makes the conventional Monte Carlo estimator for such quantities biased. In this paper, we show how such quantities can be estimated without bias. However, our approach typically increases the variance. Thus,...
We present general principles for the design and analysis of unbiased Monte Carlo estimators for quantities such as α = g(E (X)), where E (X) denotes the expectation of a (possibly multidimensional) random variable X, and g(·) is a given deterministic function. Our estimators possess finite work-normalized variance under mild regularity conditions such as local twice differentiability of g(·) and...
In this paper, we introduce a new approach to constructing unbiased estimators when computing expectations of path functionals associated with stochastic differential equations (SDEs). Our randomization idea is closely related to multi-level Monte Carlo and provides a simple mechanism for constructing a finite variance unbiased estimator with “square root convergence rate” whenever one has available...
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