Counting observations: A note on state estimation sensitivity with an L1-bound

Let (X-t, Y-t) be a pure jump Markov process: the state X-t takes real values and the observation Y-t is a counting process. The two processes are allowed to have common jump times. Let phi (X((.))) be a functional of the state trajectory restricted to the time interval [0, T]. If we change the infinitesimal parameters and/or the initial distribution, then we introduce an error in computing the conditional law of phi (X((.))) given the observation up to time T. In this paper we give an explicit L-1-bound for this error.