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March 2016 Perturbation analysis of inhomogeneous finite Markov chains
Bernd Heidergott, Haralambie Leahu, Andreas Löpker, Georg Pflug
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Adv. in Appl. Probab. 48(1): 255-273 (March 2016).

Abstract

In this paper we provide a perturbation analysis of finite time-inhomogeneous Markov processes. We derive closed-form representations for the derivative of the transition probability at time t, with t > 0. Elaborating on this result, we derive simple gradient estimators for transient performance characteristics either taken at some fixed point in time t, or for the integrated performance over a time interval [0 , t]. Bounds for transient performance sensitivities are presented as well. Eventually, we identify a structural property of the derivative of the generator matrix of a Markov chain that leads to a significant simplification of the estimators.

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Bernd Heidergott. Haralambie Leahu. Andreas Löpker. Georg Pflug. "Perturbation analysis of inhomogeneous finite Markov chains." Adv. in Appl. Probab. 48 (1) 255 - 273, March 2016.

Information

Published: March 2016
First available in Project Euclid: 8 March 2016

zbMATH: 1337.60181
MathSciNet: MR3473577

Subjects:
Primary: 60J27
Secondary: 65C05

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 1 • March 2016
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