Stochastic flows on a countable set: Convergence in distribution |
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Authors: | R W R Darling Arunava Mukherjea |
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Institution: | (1) Mathematics Department, University of South Florida, 33620-5700 Tampa, Florida |
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Abstract: | Consider a sequenceF
1,F
2,... of i.i.d. random transformations from a countable setV toV. Such a sequence describes a discrete-time stochastic flow onV, in which the position at timen of a particle that started at sitex isM
n(x), whereM
n
=F
n
F
n–1
F
1. We give conditions on the law ofF
1 for the sequence (M
n) to be tight, and describe the possible limiting law. an example called the block charge model is introduced. The results can be formulated as a statement about the convergence in distribution of products of infinite-dimensional random stochastic matrices. In practical terms, they describe the possible equilibria for random motions of systems of particles on a countable set, without births or deaths, where each site may be occupied by any number of particles, and all particles at a particular site move together. |
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Keywords: | Stochastic flow infinite particle system tightness equilibrium topological semigroup random transformation block charge model |
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