Optimal Sequential Estimation for Ergodic Birth‐Death Processes

Abstract

SUMMARY For ergodic birth-death processes a lower bound for the variance of an unbiased estimator of a function of birth and death parameters is obtained under an arbitrary stopping rule. All efficiently estimable functions and closed efficient sampling schemes are characterized. The processes treated here include random walk with reflecting barriers, immigration-death process, M/M/1 and MIMIS queues with limited or unlimited waiting space.