Sequential control variates for functionals of Markov processes

Using a sequential control variates algorithm, we compute Monte Carlo approximations of solutions of linear partial differentia equations connected to linear Markov processes by the Feynman-Kac formula. It includes diffusio processes with or without absorbing/reflectin boundary and jump processes. We prove that the bias and the variance decrease geometrically with the number of steps of our algorithm. Numerical examples show the efficienc of the method on elliptic and parabolic problems.