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Cycle time of stochastic max-plus linear systems.


 
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1. Title Title of document Cycle time of stochastic max-plus linear systems.
 
2. Creator Author's name, affiliation, country Glenn Merlet; LIAFA CNRS-Paris 7
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) law of large numbers; subadditivity; Markov chains; max-plus; stochastic recursive sequences; products of random matrices
 
3. Subject Subject classification Primary 60F15, 93C65; Secondary 60J10; 90B15; 93D209
 
4. Description Abstract We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra. This type of recursive sequences are frequently used in applied probability as they model many systems as some queueing networks, train and computer networks, and production systems. We give a necessary condition for the recursive sequences to satisfy a strong law of large numbers, which proves to be sufficient when the matrices are i.i.d. Moreover, we construct a new example, in which the sequence of matrices is strongly mixing, that condition is satisfied, but the recursive sequence do not converges almost surely.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) JSPS
 
7. Date (YYYY-MM-DD) 2008-03-10
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/488
 
10. Identifier Digital Object Identifier 10.1214/EJP.v13-488
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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