Greven A (1984)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 1984
Publisher: Institute of Mathematical Statistics (IMS)
Book Volume: 12
Pages Range: 760-767
Journal Issue: 3
The coupled branching process (it') is a Markov process on (M)s
(S = ad) with initial distribution t and the following time evolution: At rate
btq(x) a particle is born at site x, which moves instantaneously to a site y
chosen with probability q (x, y). All particles at a site die at rate pd, individual
particles die independent from each other at rate (1 - p)d. Furthermore, all
particles perform independent continuous time random walks with kernel
p(x, y). We consider here the case b = d and the symmetrized kernels p', q are
transient.
We show that the measures +([( +[a'itx])), (a E R+, X E Rd) converge
weakly for t - X to VT(y,X). Here v, is the invariant measure of the process
with:Ev,(n(x)) = p and which is also extremal in the set of all translationin-
variant invariant measures of the process. The density profile T(a, x) is
calculated explicitly; it is governed by the diffusion equation.
APA:
Greven, A. (1984). The hydrodynamical behavior of the coupled branching process. Annals of Probability, 12(3), 760-767.
MLA:
Greven, Andreas. "The hydrodynamical behavior of the coupled branching process." Annals of Probability 12.3 (1984): 760-767.
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