Large deviations of a forced velocity jump process with a Hamilton-Jacobi approach

Nils Caillerie

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arXiv · 1710.10620

Large deviations of a forced velocity jump process with a Hamilton-Jacobi approach

Nils Caillerie

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Abstract

We study the dispersion of a particle whose motion dynamics can be described by a forced velocity jump process. To investigate large deviations results, we study the Chapman-Kolmogorov equation of this process in the hyperbolic scaling (t,x,v) -> (t/epsilon,x/epsilon,v) and then, perform a Hopf-Cole transform which gives us a kinetic equation on a potential. We prove the convergence of this potential to the solution of a Hamilton-Jacobi equation. The hamiltonian can have a C1 singularity, as was previously observed in this kind of studies. This is a preliminary work before studying spreading results for more realistic processes.

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Nils Caillerie. 2017-10-29. Large deviations of a forced velocity jump process with a Hamilton-Jacobi approach. https://arxiv.org/abs/1710.10620

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