In this paper we develop and analyze the stochastic collocation method for
solving the time-dependent Maxwell’s equations with random coefficients and subject
to random initial conditions. We provide a rigorous regularity analysis of the solution
with respect to the random variables. To our best knowledge, this is the first theoretical
results derived for the standard Maxwell’s equations with random inputs. The rate of
convergence is proved depending on the regularity of the solution. Numerical results
are presented to confirm the theoretical analysis.