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Asymptotic results for non-linear processes of the McKean tagged-molecule type
Published online by Cambridge University Press: 14 July 2016
Abstract
McKean's tagged-molecule process is a non-linear homogeneous two-state Markov chain in continuous time, constructed with the aid of a binary branching process. For each of a large class of branching processes we construct a similar process. The construction is carefully done and the weak homogeneity is deduced. A simple probability argument permits us to show convergence to the equidistribution (½, ½) and to note that this limit is a strong equilibrium. A non-homogeneous Markov chain result is also used to establish the geometric rate of convergence. A proof of a Boltzmann H-theorem is also established.
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- Copyright © Applied Probability Trust 1986
Footnotes
Research supported in part by NSERC, Canada, under Grant No A-5365 and in part by a grant of Formation de Chercheurs et Actions Concertées, Gouvernement du Québec.