Berzunza, Gabriel, Sturm, Anja and Winter, Anita
(2018)
Trait-dependent branching particle systems with competition and multiple
offspring.
Electronic Journal of Probability, 26 (none).
Abstract
In this work we model the dynamics of a population that evolves as a continuous time branching process with a trait structure and ecological interactions in form of mutations and competition between individuals. We generalize existing microscopic models by allowing individuals to have multiple offspring at a reproduction event. Furthermore, we allow the reproduction law to be influenced both by the trait type of the parent as well as by the mutant trait type. We look for tractable large population approximations. More precisely, under some natural assumption on the branching and mutation mechanisms, we establish a superprocess limit as solution of a well-posed martingale problem. Standard approaches do not apply in our case due to the lack of the branching property, which is a consequence of the dependency created by the competition between individuals. For showing uniqueness we therefore had to develop a generalization of Dawson's Girsanov Theorem that may be of independent interest.
| Item Type: | Article |
|---|---|
| Additional Information: | 52 |
| Uncontrolled Keywords: | math.PR, math.PR, 60J80, 60J68, 60K35 |
| Divisions: | Faculty of Science and Engineering > School of Physical Sciences |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 04 Mar 2022 11:31 |
| Last Modified: | 17 Mar 2024 09:05 |
| DOI: | 10.1214/21-ejp707 |
| Open Access URL: | https://doi.org/10.1214/21-EJP707 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3150107 |
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