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dc.contributor.authorBouin, Emeric
dc.contributor.authorCalvez, Vincent
HAL ID: 11087
ORCID: 0000-0002-3674-1965
dc.contributor.authorGrenier, Emmanuel
dc.contributor.authorNadin, Grégoire
HAL ID: 4575
dc.subjectLarge deviations
dc.subjectPiecewise Deterministic Markov Processes
dc.subjectHamilton-Jacobi equations
dc.subjectViscosity solutions
dc.subjectScaling limits
dc.subjectFront acceleration
dc.titleLarge deviations for velocity-jump processes and non-local Hamilton-Jacobi equations
dc.typeDocument de travail / Working paper
dc.description.abstractenWe establish a large deviation theory for a velocity jump process, where new random velocities are picked at a constant rate from a Gaussian distribution. The Kolmogorov forward equation associated with this process is a linear kinetic transport equation in which the BGK operator accounts for the changes in velocity. We analyse its asymptotic limit after a suitable rescaling compatible with the WKB expansion. This yields a new type of Hamilton Jacobi equation which is non local with respect to velocity variable. We introduce a dedicated notion of viscosity solution for the limit problem, and we prove well-posedness in the viscosity sense. The fundamental solution is explicitly computed, yielding quantitative estimates for the large deviations of the underlying velocity-jump process à la Freidlin-Wentzell. As an application of this theory, we conjecture exact rates of acceleration in some nonlinear kinetic reaction-transport equations.
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphine

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