A Low Bias Steady-State Estimator for Equilibrium Processes

P. W. Glynn

Technical Report, Mathematics Research Center, University of Wisconsin, Madison

This paper concerns the steady state structure of equilibrium processes; an equilibrium process is a generalization of regenerative process which is useful for studying Harris recurrent Markov chains. Specifically, if X=(X(t) : t≥0) is a real valued non arithmetic equilibrium process, then an asymptotic relation of the form\int_0^t EX(s)ds= αt+β+o(1) as t->∞ is obtained. This asymptotic expression is then used to obtain a Monte Carlo estimator for the steady state mean alpha which has lower bias than the traditional sample mean estimator \bar{X̄}(t). The reduced bias is obtained without adversely affecting the asymptotic convergence rate.