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Lyapunov Conditions for Differentiability of Markov Chain Expectations

Author

Listed:
  • Chang-Han Rhee

    (Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

  • Peter W. Glynn

    (Management Science and Engineering, Stanford University, Stanford, California 94305)

Abstract

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.

Suggested Citation

  • Chang-Han Rhee & Peter W. Glynn, 2023. "Lyapunov Conditions for Differentiability of Markov Chain Expectations," Mathematics of Operations Research, INFORMS, vol. 48(4), pages 2019-2042, November.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:4:p:2019-2042
    DOI: 10.1287/moor.2022.1328
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