Lyapunov Conditions for Differentiability of Markov Chain Expectations
成果类型：
Article
署名作者：
Rhee, Chang-Han; Glynn, Peter W.
署名单位：
Northwestern University; Stanford University
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2022.1328
发表日期：
2023
页码：
2019-2042
关键词：
摘要：
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 and their continuity 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 smoothness 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.