Rank-dependent GaltonWatson processes and their pathwise duals
Journal article, 2018

We introduce a modified GaltonWatson process using the framework of an infinite system of particles labelled by (x,t), where x is the rank of the particle born at time t. The key assumption concerning the offspring numbers of different particles is that they are independent, but their distributions may depend on the particle label (x,t). For the associated system of coupled monotone Markov chains, we address the issue of pathwise duality elucidated by a remarkable graphical representation in which the trajectories of the primary Markov chains and their duals coalesce to form forest graphs on a two-dimensional grid.

Siegmund's duality

Graphical representation

birth-death process

dual forest

linear-fractional reproduction


Serik Sagitov

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Jonas Jagers

Student at Chalmers

Advances in Applied Probability

0001-8678 (ISSN) 1475-6064 (eISSN)

Vol. 50 A 229-239

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