Stochastic Bounds with a Low Rank Decomposition

Ana Bušić (1, 2) , Jean-Michel Fourneau (3) , Mouad Ben Mamoun (4)

1 DYOGENE - Dynamics of Geometric Networks
2 LINCS - Laboratory of Information, Network and Communication Sciences
3 MAGMAT - Models, Algorithms, and Games for Molecules Analysis and Telecommunications
4 UM5 - Université Mohammed V de Rabat [Agdal]

We investigate how we can bound a discrete time Markov chain (DTMC) by a stochastic matrix with a low rank decomposition. In the first part of the article, we show the links with previous results for matrices with a decomposition of size 1 or 2. Then we show how the complexity of the analysis for steady-state and transient distributions can be simplified when we take into account the decomposition. Finally, we show how we can obtain a monotone stochastic upper bound with a low rank decomposition.

Mots clés: Algorithms; Discrete time Markov chains; Low rank approximation; Numerical computations; Stochastic bounds

Domaines: Mathématique discrète [cs.DM]; Performance et fiabilité [cs.PF]

Ana Bušić, Jean-Michel Fourneau, Mouad Ben Mamoun. Stochastic Bounds with a Low Rank Decomposition. Stochastic Models, 2014, Special Issue on the Eighth International Conference on Matrix-Analytic Methods in Stochastic Models, 30 (4), pp.494-520. ⟨10.1080/15326349.2014.954132⟩. ⟨hal-01099891⟩