# Tensor approach to mixed high-order moments of absorbing Markov chains

1 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Moments of absorbing Markov chain are considered. First moments and non-mixed second moments are determined in classical textbooks such as the book of J. Kemeny and J. Snell Finite Markov Chains''. The reason is that the first moments and the non-mixed second moments can be easily expressed in a matrix form. Since the representation of mixed moments of higher orders in a matrix form is not straightforward, if ever possible, they were not calculated. The gap is filled by this paper. Tensor approach to the mixed high-order moments is proposed and compact closed-form expressions for the moments are discovered.
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https://hal.inria.fr/inria-00426763
Contributor : Danil Nemirovsky <>
Submitted on : Wednesday, October 28, 2009 - 11:46:36 AM
Last modification on : Tuesday, January 9, 2018 - 10:50:02 AM
Long-term archiving on: : Tuesday, October 16, 2012 - 12:46:17 PM

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RR-7072.pdf
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• HAL Id : inria-00426763, version 1

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Danil Nemirovsky. Tensor approach to mixed high-order moments of absorbing Markov chains. [Research Report] RR-7072, 2009. ⟨inria-00426763v1⟩

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