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We study the derivation of a scalar conservation law with stochastic forcingstarting from a stochastic BGK model with a high-field scaling. We prove theconvergence to a new kinetic formulation where appears a modified Maxwellian.We deduce from it the existence of a weak solution to the scalar conservationlaw with stochastic forcing. We establish that this solution satisfies someKrushkov-like entropy relations.

High-Field Limit from a Stochastic BGK Model to a Scalar Conservation Law with Stochastic Forcing