## Perturbation analysis of inhomogeneous finite Markov chains.(English)Zbl 1337.60181

Summary: 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.

### MSC:

 60J27 Continuous-time Markov processes on discrete state spaces 60J35 Transition functions, generators and resolvents 62M05 Markov processes: estimation; hidden Markov models 65C05 Monte Carlo methods
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### References:

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