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.In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes. In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only be solved numerically via a time discretization. We develop, based upon the approach in Lemaire, Thieullen, and Thomas Adv. Appl. Probab., 52 (2020), pp. 138–172, a new particle and multilevel particle filter (MLPF) in order to approximate the filter associated to the discretized ODE. We provide a bound on the mean square error associated to the MLPF which provides guidance on setting the simulation parameters of the algorithm and implies that significant computational gains can be obtained versus using a particle filter. Our theoretical claims are confirmed in several numerical examples.Keywordsmultilevel Monte Carloparticle filtersPDMPsfilteringMSC codes65C0565C2065C3565C4060J27
Jasra et al. (Fri,) studied this question.