IPA for Stationary Problems

In this paper, we develop a unified theory of IPA estimators for steady-state performance characteristics. Our goal is to clarify how infinitesimal perturbation analysis can be systematically connected to a measure-valued differentiation framework for the underlying Markov chain dynamics. Traditionally, the asymptotic behavior of gradient estimators has been studied by analyzing the estimators themselves. Here, we take a different perspective. We show that by clearly separating the level at which arguments are made, either at the sample-path level, where IPA is usually formulated, or at the operator/measure level, where Markov chain differentiation is naturally expressed, one can combine the strengths of both approaches. Our framework helps bridge two established streams of research and contributes a more general understanding of IPA for steady-state problems.