The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
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,...
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...
Infinite-horizon average-cost Markov decision processes are of interest in many scenarios. A dynamic programming algorithm, called the relative value iteration, is used to compute the optimal value function. For large state spaces, this often runs into difficulties due to its computational burden. We propose a simulation-based dynamic program called empirical relative value iteration (ERVI). The idea...
We analyze the convergence to equilibrium of one-dimensional reflected Brownian motion (RBM) and compute a number of related initial transient formulae. These formulae are of interest as approximations to the initial transient for queueing systems in heavy traffic, and help us to identify settings in which initialization bias is significant. We conclude with a discussion of mean square error for RBM...
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...
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...
This paper models the detection of the initial transient in a steady-state simulation problem as a change point hypothesis testing problem. We introduce two new hypothesis tests for the initial transient, each of which is based on the Brownian bridge process and each of which is a composite test that involves testing against infinitely many alternatives (that depend on the duration of the transient...
Simulation-based ordinal optimization has frequently relied on large deviations analysis as a theoretical device for arguing that it is computationally easier to identify the best system out of d alternatives than to estimate the actual performance of a given design. In this paper, we argue that practical implementation of these large deviations-based methods need to estimate the underlying large...
The problem of estimating discrete time stochastic processes by autoregressive (AR) models is encountered in many applications. The present paper explores the asymptotic behavior of the spectral density of such approximations. It is shown that under certain assumptions on the spectral density and the covariance sequence of the original process, the spectral density of the approximating autoregressive...
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...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.