The distribution of the spine of a Fleming-Viot type process

Mariusz Bieniek; Krzysztof Burdzy

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arXiv · 1507.06855

The distribution of the spine of a Fleming-Viot type process

Mariusz Bieniek·Krzysztof Burdzy

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Abstract

We show uniqueness of the spine of a Fleming-Viot particle system under minimal assumptions on the driving process. If the driving process is a continuous time Markov process on a finite space, we show that asymptotically, when the number of particles goes to infinity, the branching rate for the spine is twice that of a generic particle in the system, and every side branch has the distribution of the unconditioned generic branching tree.

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Mariusz Bieniek, Krzysztof Burdzy. 2015-07-24. The distribution of the spine of a Fleming-Viot type process. https://arxiv.org/abs/1507.06855

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