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

Romain Azaïs and Alexandre Genadot

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 8, 1812-1829

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.

Date: 2018
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DOI: 10.1080/03610926.2017.1327072

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