Section: New Results

Non parametric estimation of conditional distribution of the interjumping times for piecewise Markov processes

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

This work gives 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 example illustrates the behavior of our estimator. This work is the object of a paper [56] submitted for publication