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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Kraaij, Richard C.¹  Mahe, Louis² 

[1] Delft Univ Technol, Dept Appl Math, Delft, Netherlands

[2] Univ Paris Saclay, CNRS, Ecole Polytech, Route Saclay, F-91128 Palaiseau, France

关键词: Large deviations;    Population dynamics;    Hamilton-Jacobi equations;    Boundary conditions;   

DOI  :  10.1016/j.spa.2020.03.013

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free