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August 2005 Equilibrium for fragmentation with immigration
Bénédicte Haas
Ann. Appl. Probab. 15(3): 1958-1996 (August 2005). DOI: 10.1214/105051605000000340


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.


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Bénédicte Haas. "Equilibrium for fragmentation with immigration." Ann. Appl. Probab. 15 (3) 1958 - 1996, August 2005.


Published: August 2005
First available in Project Euclid: 15 July 2005

zbMATH: 1093.60050
MathSciNet: MR2152250
Digital Object Identifier: 10.1214/105051605000000340

Primary: 60B10 , 60J25 , 60J55 , 82C21

Keywords: fragmentation , immigration , stationary distribution

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.15 • No. 3 • August 2005
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