Branching trees I: concatenation and infinite divisibility

Glode P, Greven A, Rippl T (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Electronic Journal of Probability Institute of Mathematical Statistics (IMS): OAJ / Institute of Mathematical Statistics

Book Volume: 24

DOI: 10.1214/19-EJP276

Abstract

The goal of this work is to decompose random populations with a genealogy in subfamilies of a given degree of kinship and to obtain a notion of infinitely divisible genealogies. We model the genealogical structure of a population by (equivalence classes of) ultrametric measure spaces (um-spaces) as elements of the Polish space U which we recall. In order to then analyze the family structure in this coding we introduce an algebraic structure on um-spaces (a consistent collection of semigroups). This allows us to obtain a path of decompositions of subfamilies of fixed kinship h (described as ultrametric measure spaces), for every depth h as a measurable functional of the genealogy.

Authors with CRIS profile

Andreas Greven Lehrstuhl für Mathematische Stochastik

Involved external institutions

Technion - Israel Institute of Technology IL Israel (IL) Institut für Mathematische Stochastik (IMS) DE Germany (DE)

How to cite

APA:

Glode, P., Greven, A., & Rippl, T. (2019). Branching trees I: concatenation and infinite divisibility. Electronic Journal of Probability, 24. https://dx.doi.org/10.1214/19-EJP276

MLA:

Glode, Patric, Andreas Greven, and Thomas Rippl. "Branching trees I: concatenation and infinite divisibility." Electronic Journal of Probability 24 (2019).

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