I am looking for a martingale representation theorem for positive semimartingales. Using the answer to this question: Martingale representation theorem for Levy processes

My best guess is (subject to integrability condition, in one dimension for simplicity): $$ M_t = M_0 + \int_0^t M_s v_s dWs + \int_0^t \int_R M_s u_s(x) \tilde{N}(ds, dx)$$

where $\tilde{N}(ds, dx)$ is the compensated measure of the underlying Lévy process, but as I said its just a guess. Is it correct? Do I need any conditions for $u_s(x)$?