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Preprints, Working Papers, ... (Preprint) Year : 2023

Spinal constructions for continuous type-space branching processes with interactions

Abstract

We consider branching processes describing structured, interacting populations in continuous time. Dynamics of each individual's characteristics and branching properties can be influenced by the entire population. We propose a spinal construction, and establish a Girsanov-type result. By combining this result with the spinal decomposition, we derive a modified continuous-time version of the Kesten-Stigum theorem that incorporates interactions. Additionally, we propose an alternative simulation approach for stochastic size-dependent populations using appropriate spine constructions.
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Dates and versions

hal-04179190 , version 1 (09-08-2023)

Licence

Public Domain

Identifiers

  • HAL Id : hal-04179190 , version 1

Cite

Charles Medous. Spinal constructions for continuous type-space branching processes with interactions. 2023. ⟨hal-04179190⟩
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