{
  "id": "1704.04203",
  "version": "v1",
  "published": "2017-04-13T16:35:03.000Z",
  "updated": "2017-04-13T16:35:03.000Z",
  "title": "Branching processes with interactions: the subcritical cooperative regime",
  "authors": [
    "Adrián González Casanova",
    "Juan Carlos Pardo",
    "José Luis Perez"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we introduce a particular family of processes with values on the nonnegative integers that model the dynamics of populations where individuals are allow to have different types of inter- actions. The types of interactions that we consider include pairwise: competition, annihilation and cooperation; and interaction among several individuals that can be consider as catastrophes. We call such families of processes branching processes with interactions. In particular, we prove that a process in this class has a moment dual which turns out to be a jump-diffusion that can be thought as the evolution of the frequency of a trait or phenotype. The aim of this paper is to study the long term behaviour of branching processes with interac- tions under the assumption that the cooperation parameter satisfies a given condition that we called subcritical cooperative regime. The moment duality property is useful for our purposes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-13T16:35:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "subcritical cooperative regime",
      "interaction",
      "long term behaviour",
      "cooperation parameter satisfies",
      "moment duality property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}