Smoothed Limit Theorems for Equilibrium Processes

P. W. Glynn and D. L. Iglehart

In Probability,Statistics, and Mathematics:  Papers in Honor of Samuel Karlin, [T.W. Anderson, K.B.T. Athreya, D.L. Iglehart, eds.].  Academic Press, Boston, 89-102 (1989)

Renewal ideas play a fundamental rule in applied probability. In particular, renewal methods are powerful tools for dealing with the asymptotic behavior of the regenerative processes that are typical of queueing and operations research applications. In this paper were survey the main results of the theory and develop some smoothed versions of the convergence theorems. These smoothed versions typically have much weaker associated regularity hypotheses than the classical version. These smoothed limit theorems are established under minimal conditions that are essentially necessary.