The filtering equations associated to a partially observed jump diffusion model \((Z_t)_{t\in [0,T]}=(X_t,Y_t)_{t\in [0,T]}\) , driven by Wiener processes and Poisson martingale measures are considered. Building on results from two preceding articles on the filtering equations, the regularity of the conditional density of the signal \(X_t\) , given observations \((Y_s)_{s\in [0,t]}\) , is investigated, when the conditional density of \(X_0\) given \(Y_0\) exists and belongs to a Sobolev space, and the coefficients satisfy appropriate smoothness and growth conditions.
