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...

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...

Compound stochastic processes are constructed by taking the superpositive of independent copies of secondary processes, each of which is initiated at an epoch of a renewal process called the primary process. Suppose there are M possible k-dimensional secondary processes...

This note considers the taboo counterpart of stationarity. A general stochastic process in two-sided time is defined to be taboo-stationary if its global distribution does not change by shifting the origin to an arbitrary non-random time in the future under taboo, that is, conditionally on some...

Necessary and sufficient conditions are established for cumulative process (associated with regenerative processes) to obey several classical limit theorems; e.g., a strong law of large numbers, a law of the iterated logarithm and a functional central limit theorem. The key random variables are...

In this paper, we study the two-sided taboo limit processes that arise when a Markov chain or process is conditioned on staying in some set A for a long period of time. The taboo limit is time-homogeneous after time 0 and time-inhomogeneous before time 0. The time-reversed limit has this same...

For a given countable partition of the range of a regenerative sequence {Xn: n [greater-or-equal, slanted] 0}, let Rn be the number of distinct sets in the partition visited by X up to time n. We study convergence issues associated with the range sequence {Rn: n [greater-or-equal, slanted] 0}....

We show that sufficient conditions in terms of moments for cumulative processes (additive functionals of regenerative processes) to satisfy the central limit theorem and the weak law of large numbers established in Glynn and Whitt (Stochastic Process. Appl. 47 (1993) 299-314) are also necessary,...