Stochastic PDE models for chiral media: Well posedness, singular limits and a priori estimates for their validity

In the present work we consider the problem of evolution of electromagnetic fields in a random chiral medium, with random external excitations. We establish the well posedness of the resulting stochastic model with additive noise, based on the Maxwell equations with nonlocal in time linear constitutive relations, as well as of a singular limit (local in time) approximative model which formally resembles the Drude-Born-Fedorov constitutive relations for chiral media. We also provide a priori estimates of the difference of the fields as predicted by both models, depending on properties of the stochastic term, the time horizon, properties of the domain, properties of the random initial data and source terms and the chirality measure of the approximative model.