Estimation of Steady-State Central Moments by the Regenerative Method of Simulation

P. W. Glynn and D. L. Iglehart

Operations Research Letters, Vol. 5,  271-276 (1986)

Let X be a positive recurrent regenerative process on state space S with steady-state distribution π. Given a function f: S-> R, we consider the problem of estimating the steady-state central moments μk(f)=∫S(f(x)-r)kπ(dx) where r is the steady-state mean of f(X(.)). We obtain strong laws, central limit theorems, and confidence intervals for our estimators, and present numerical results.