Well-posedness of Hamilton-Jacobi equations in population dynamics and applications to large deviations
| Autor: | Richard C. Kraaij, Louis Mahé |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Large class Population dynamics Population Mathematical proof 01 natural sciences Hamilton–Jacobi equation 010104 statistics & probability symbols.namesake Mathematics::Probability FOS: Mathematics Applied mathematics Quantitative Biology::Populations and Evolution Hamilton–Jacobi equations 0101 mathematics education Mathematics education.field_of_study Boundary conditions 49L25 60F10 60J80 92D25 Applied Mathematics Probability (math.PR) 010102 general mathematics Large deviations Modeling and Simulation symbols Large deviations theory Hamiltonian (quantum mechanics) Well posedness Mathematics - Probability |
| Zdroj: | Stochastic Processes and their Applications, 130(9) |
| ISSN: | 0304-4149 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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