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

Richard C. Kraaij, Louis Mahé

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)5453-5491
Number of pages39
JournalStochastic Processes and their Applications
Volume130
Issue number9
DOIs
Publication statusPublished - 2020

Keywords

  • Boundary conditions
  • Hamilton–Jacobi equations
  • Large deviations
  • Population dynamics

Fingerprint Dive into the research topics of 'Well-posedness of Hamilton–Jacobi equations in population dynamics and applications to large deviations'. Together they form a unique fingerprint.

Cite this