Limit theorems for path-functionals of regenerative processes

Douglas R. Miller

Stochastic Processes and their Applications, 1974, vol. 2, issue 2, 141-161

Abstract: Regenerative processes were defined and investigated by Smith [12]. These processes have limiting distributions under very mild regularity conditions. In certain applications, such as shot-noise processes and some queueing problems, it is of interest to consider path-functionals of regenerative processes. We seek to extend the nice asymptotic properties of regenerative processes to path-functionals of regenerative processes. We show that these more general processes converge to a "steady-state" process in a certain weak sense. This is applied to show convergence of shot-noise processes. We also present a Blackwell theorem for path-functionals of regenerative processes.

Date: 1974
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