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This letter presents a novel methodology for the stochastic simulation of interconnects illuminated by random external fields. The proposed strategy is based on the polynomial expansion of the classical forcing terms describing the coupling of external fields onto transmission lines. This method turns out to be accurate and is much faster than traditional solutions like the Monte Carlo (MC) method in determining statistical parameters of interest. The advantages of the proposed approach are demonstrated by means of comparisons with MC simulations in the case of incident plane waves with arbitrary amplitude, polarization, or direction of incidence.