A new characterization of the jump rate for piecewise-deterministic Markov processes with discrete transitions

Romain Azaïs (1, 2) , Alexandre Genadot (3, 4)

1 BIGS - Biology, genetics and statistics
2 IECL - Institut Élie Cartan de Lorraine
3 IMB - Institut de Mathématiques de Bordeaux
4 CQFD - Quality control and dynamic reliability

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 nonparametric 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.

Mots clés: Piecewise-deterministic Markov process; Jump rate; Estimation; Discrete transitions

Domaines: Méthodologie [stat.ME]

Romain Azaïs, Alexandre Genadot. A new characterization of the jump rate for piecewise-deterministic Markov processes with discrete transitions. Communications in Statistics - Theory and Methods, 2018, 47 (8), pp.1812-1829. ⟨10.1080/03610926.2017.1327072⟩. ⟨hal-01334847⟩