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We investigate the regularity of the law of Wong-Zakai-type approximationsfor It\^o stochastic differential equations. These approximations solve randomdifferential equations where the diffusion coefficient is Wick-multiplied bythe smoothed white noise. Using a criteria based on the Malliavin calculus weestablish absolute continuity and a Fokker-Planck-type equation solved in thedistributional sense by the density. The parabolic smoothing effect typical ofthe solutions of It\^o equations is lacking in this approximated framework;therefore, in order to prove absolute continuity, the initial condition of therandom differential equation needs to possess a density itself.

Absolute continuity and Fokker-Planck equation for the law of Wong-Zakai approximations of It\^o's stochastic differential equations