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

We study the dispersion of a particle whose motion dynamics can be described by forced velocity jump process. To investigate large deviations results, we Kolmogorov forward equation this process in hyperbolic scaling (t,x,v)→(t/ε,x/ε,v) and then, perform Hopf–Cole transform which gives us kinetic on potential. prove convergence potential as ε→0 to solution Hamilton–Jacobi equation. The hamiltonian have C 1 singularity, was previously observed kind studies. This is preliminary work before studying spreading results for more realistic processes.