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...

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...

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,...