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Calculating the variance in Markov-processes with random reward.

Francisco Benito (1982)

Trabajos de Estadística e Investigación Operativa

In this article we present a generalization of Markov Decision Processes with discreet time where the immediate rewards in every period are not deterministic but random, with the two first moments of the distribution given.Formulas are developed to calculate the expected value and the variance of the reward of the process, formulas which generalize and partially correct other results. We make some observations about the distribution of rewards for processes with limited or unlimited horizon and...

Central limit theorem for hitting times of functionals of Markov jump processes

Christian Paroissin, Bernard Ycart (2004)

ESAIM: Probability and Statistics

A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications.

Central limit theorem for hitting times of functionals of Markov jump processes

Christian Paroissin, Bernard Ycart (2010)

ESAIM: Probability and Statistics

A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications.

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