Dynamics and Endogeny for recursive processes on trees

2005/06/02 by Jon Warren, Warren, Jon
Mathematics · #60J25 #60J80 #60K35 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J25 #msc:60J80 #msc:60K35

paper · pdf · doi:10.48550/arxiv.math/0506038

15 pages

arxiv created 2005/06/02 · arxiv updated 2009/12/01

Abstract

We consider stochastic processes indexed by the vertices of an infinite binary tree having a simple recursive structure. The value at any vertex is some fixed function of the values at the two daughter vertices together with some independent innovation. Endogeny means the innovations are generating. When endogeny does not hold there exist dynamics in which the innovations are held fixed while some additional randomness on the boundary of the tree is perturbed.

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