Well-posedness of Hamilton–Jacobi equations in population dynamics and applications to large deviations

Journal Article (2020)
Author(s)

R.C. Kraaij (TU Delft - Applied Probability)

Louis Mahé (University Paris-Saclay)

Research Group
Applied Probability
Copyright
© 2020 R.C. Kraaij, Louis Mahé
DOI related publication
https://doi.org/10.1016/j.spa.2020.03.013
More Info
expand_more
Publication Year
2020
Language
English
Copyright
© 2020 R.C. Kraaij, Louis Mahé
Research Group
Applied Probability
Issue number
9
Volume number
130
Pages (from-to)
5453-5491
Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Abstract

We prove Freidlin–Wentzell type large deviation principles for various rescaled models in populations dynamics that have immigration and possibly harvesting: birth–death processes, Galton–Watson trees, epidemic SI models, and prey–predator models. The proofs are carried out using a general analytic approach based on the well-posedness of a class of associated Hamilton–Jacobi equations. The notable feature for these Hamilton–Jacobi equations is that the Hamiltonian can be discontinuous at the boundary. We prove a well-posedness result for a large class of Hamilton–Jacobi equations corresponding to one-dimensional models, and give partial results for the multi-dimensional setting.

Files

Population_HJ_2020_01_09.pdf
(pdf | 0.812 Mb)
- Embargo expired in 24-07-2022