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

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.

References in corpus (4)

• Dynamical moderate deviations for the Curie-Weiss model
• Classical large deviations theorems on complete Riemannian manifolds
• The exponential resolvent of a Markov process and large deviations for Markov processes via Hamilton-Jacobi equations
• A general convergence result for viscosity solutions of Hamilton-Jacobi equations and non-linear semigroups

Cited by in corpus (2)

• Large deviations and dynamical phase transitions in stochastic chemical networks
• Comparison Principle for Hamilton-Jacobi-Bellman Equations via a Bootstrapping Procedure