Nonparametric estimation of the conditional distribution of the   inter-jumping times for piecewise-deterministic Markov processes
  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. 
Romain Aza\"is, Fran\c{c}ois Dufour, and Anne G\'egout-Petit
math.ST stat.TH