Equilibrium for fragmentation with immigration

Details Equilibrium for fragmentation with immigration Equilibrium for fragmentation with immigration

2005-08-24

arxiv.org/abs/math/0508462v1

Annals of Applied Probability 2005, Vol. 15, No. 3, 1958-1996

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051605000000340 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

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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