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Equilibrium for fragmentation with immigration

Haas, Bénédicte (2005), Equilibrium for fragmentation with immigration, The Annals of Applied Probability, 15, 3, p. 1958-1996. http://dx.doi.org/10.1214/105051605000000340

Type
Article accepté pour publication ou publié
Date
2005
Journal name
The Annals of Applied Probability
Volume
15
Number
3
Publisher
Institute of Mathematical Statistics
Pages
1958-1996
Publication identifier
Metadata
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Author(s)
Haas, Bénédicte
Abstract (EN)
This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and absence of stationary distributions are established and uniqueness is proved. Also, convergence rates to the stationary distribution are given. Linear equations which are the deterministic counterparts of fragmentation with immigration processes are next considered. As in the stochastic case, existence and uniqueness of solutions, as well as existence and uniqueness of stationary solutions, are investigated.
Subjects / Keywords
Fragmentation; Immigration; Stationary distribution; Probabilités