2017/07/12 by Chang Han Rhee, Peter W. Glynn, Rhee, Chang-Han +1 · 1 citation
Computer Science · Decision Sciences · Mathematics · #60J05 #Bayesian Modeling and Causal Inference #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.1707.03870
openalex publication_date 2017/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a family of Markov chains whose transition dynamics are affected by model parameters. Understanding the parametric dependence of (complex) performance measures of such Markov chains is often of significant interest. The derivatives of the performance measures w.r.t. the parameters play important roles, for example, in numerical optimization of the performance measures, and quantification of the uncertainties in the performance measures when there are uncertainties in the parameters from the statistical estimation procedures. In this paper, we establish conditions that guarantee the differentiability of various types of intractable performance measures---such as the stationary and random horizon discounted performance measures---of general state space Markov chains and provide probabilistic representations for the derivatives.