The principal problem associated with steady-state simulation is the estimation of the variance term in an associated central limit theorem. This paper develops several strongly consistent estimates for this term using the strong approximations available for Brownian motion. A comparison of...

Importance sampling is one of the classical variance reduction techniques for increasing the efficiency of Monte Carlo algorithms for estimating integrals. The basic idea is to replace the original random mechanism in the simulation by a new one and at the same time modify the function being...

In financial markets traders often protect their position from a significant decline by using a trailing stop. Assume the trader is long the market (owns the security). A trailing stop is an order to sell the security at the market, if the price of the security drops to the stop price. The stop...

An inventory stock record is in error when the stock record is not in agreement with the physical stock. Such discrepancies may be introduced due to time lags between flow of information and material, pilferage, incorrect unit of issue, inaccurate physical inventory counts, etc. The primary...

The optimal ordering policy for a n-period dynamic inventory problem in which the ordering cost is linear plus a fixed reorder cost and the other one-period costs are convex is characterized by a pair of critical numbers, (s_n, S_n); see Scarf, [4]. In this paper we give bounds for the sequences...

In this paper we consider a firm that must make a production decision and a capital decision at periodic intervals of time. The cost of production is assumed to be convex and the firm is allowed to hold inventories. For a class of inventory and capital costs the optimal production and capital...

In this paper we consider the dynamic inventory problem in which the demand distribution possesses a density belonging to either the exponential or range family of densities and having an unknown parameter. An a priori density is chosen for the unknown parameter. Using a Bayesian estimation...

The previous papers in this series developed a methodology for obtaining from certain simulations confidence intervals for parameters associated with the steady-state distribution. This methodology required the simulations to contain an embedded renewal process at whose epochs the simulation...

Response to Remarks of M. Hofri (Hofri, Micha. 1976. Note--Re: Michael A. Crane, Donald L. Iglehart, "Simulating stable stochastic systems, IV: Approximation techniques". Management Sci. 22 (8) 913).

Weak convergence of probability measures on function spaces has been active area of research in recent years. While the theory has a somewhat abstract base, it is extremely useful in a wide variety of problems and we believe has much to offer to applied probability. Our aim in this survey paper...