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

Romain Azaïs (1, 2) , François Dufour (1, 2) , Anne Gégout-Petit (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 CQFD - Quality control and dynamic reliability

This paper presents 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.

Domaines: Théorie [stat.TH]

Romain Azaïs, François Dufour, Anne Gégout-Petit. Nonparametric estimation of the conditional distribution of the inter-jumping times for piecewise-deterministic Markov processes. 2012. ⟨hal-00759064⟩