A new characterization of the jump rate for piecewise-deterministic Markov processes with discrete transitions. Issue 8 (18th April 2018) - Azaïs, Romain; Genadot, Alexandre
ABSTRACT: Piecewise-deterministic Markov processes form a general class of non diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate of such a process with discrete transitions. We deduce from this result a non parametric technique for estimating this feature of interest. We state the uniform convergence in probability of the estimator. The methodology is illustrated on a numerical example.