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This paper contrasts exact simulation against exact estimation in two different computational settings, namely that of numerical solution of stochastic differential equations and also in the context of equilibrium calculations for Markov chains. Both exact simulation and exact estimation methods can provide unbiased estimators capable of converging at square root rate in the computational effort c...
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,...
Long-run stochastic stability is a precondition for applying steady-state simulation output analysis methods to a stochastic Petri Net (SPN), and is of interest in its own right. A fundamental stability requirement for an irreducible SPN is that the markings of the net be recurrent, in that the marking process visits each marking infinitely often with probability 1. We study recurrence properties...
We propose a new algorithm for identifying the duration of the initial transient for a regenerative stochastic process. The algorithm involves re-sampling of the simulated cycles, and therefore has a “bootstrap” flavor. The paper includes a derivation of the estimator for the duration of the transient that offers theoretical support for its validity, and provides a preliminary numerical investigation...
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