Sensitivity Analysis for Stationary Probabilities of a Markov Chain

P. W. Glynn

Proceedings of the 4th Army Conference on Applied Mathematics and Computing, 917-932 (1986)

This paper considers the problem of evaluating the sensitivity of a steady state cost α(θ) to underlying uncertainty in a parameter vector θ governing the probabilistic dynamics of the system under consideration. We show that the gradient ∇α(θ) plays a fundamental role in the parametric statistical theory for Markov processes. We then survey numerical methods available for evaluating ∇α(θ) and introduce a new Monte Carlo estimator for ∇α(θ), which is applicable to Markov processes of substantial generality.