Section: New Results

Nonparametric estimation of the conditional distribution of the inter-jumping times for piecewise-deterministic markov processes

Participants : Romain Azais, François Dufour, Anne Gégout-Petit.

Piecewise-deterministic Markov process, ergodicity of Markov chains, nonparametric estimation, jump rate estimation, Nelson-Aalen estimator, asymptotic consistency

In this work, we present a nonparametric method for estimating the conditional density associated to the jump rate of a piecewise-deterministic Markov process. In our framework, the estimation needs only one observation of the process within a long time interval. Our method relies on a generalization of Aalen?s multiplicative intensity model. We prove the uniform consistency of our estimator, under some reasonable assumptions related to the primitive characteristics of the process. A simulation study illustrates the behavior of our estimator.

It has been accepted for publication in Scandinavian Journal of Statistics [17] .