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A path-valued Markov process indexed by the ancestral mass

Abstract

A family of Feller branching diffusions ZxZ^x, x≥0x \ge 0, with nonlinear drift and initial value xx can, with a suitable coupling over the {\em ancestral masses} xx, be viewed as a path-valued process indexed by xx. For a coupling due to Dawson and Li, which in case of a linear drift describes the corresponding Feller branching diffusion, and in our case makes the path-valued process Markovian, we find an SDE solved by ZZ, which is driven by a random point measure on excursion space. In this way we are able to identify the infinitesimal generator of the path-valued process. We also establish path properties of x↦Zxx\mapsto Z^x using various couplings of ZZ with classical Feller branching diffusions.Comment: 23 pages, 1 figure. This version will appear in ALEA. Compared to v1, it contains amendmends mainly in Sec. 2 and in the proof of Proposition 4.

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    Last time updated on 11/11/2016