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

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  • Kraaij, Richard C.
  • Mahé, Louis

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.

Suggested Citation

  • Kraaij, Richard C. & Mahé, Louis, 2020. "Well-posedness of Hamilton–Jacobi equations in population dynamics and applications to large deviations," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5453-5491.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:9:p:5453-5491
    DOI: 10.1016/j.spa.2020.03.013
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    References listed on IDEAS

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    1. Adam Shwartz & Alan Weiss, 2005. "Large Deviations with Diminishing Rates," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 281-310, May.
    2. Kraaij, Richard C. & Redig, Frank & Versendaal, Rik, 2019. "Classical large deviation theorems on complete Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4294-4334.
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