The Covariance Function of a Regenerative Process

P. W. Glynn

Technical Report, Department of Engineering-Economic Systems and Operations Research, Stanford University, (1997)

In this paper, we develop regenerative representations for the covariance function of both a non-delayed regenerative process and a stationary regenerative process. These results are used to obtain conditions under which the lag-t covariance vanishes as t → ∞, together with associated rates of convergence. The spectral density of a stationary regenerative process is then calculated explicitly in terms of quantities expressed over regenerative cycles. The paper concludes with an application of the theory developed here to the steady-state simulation problem.