  Counting processes often written $N=(N_t)_{t\in\mathbb{R}^+}$ are used in
several applications of biostatistics, notably for the study of chronic
diseases. In the case of respiratory illness it is natural to suppose that the
count of the visits of a patient can be described by such a process which
intensity depends on environmental covariates. Cox processes (also called
doubly stochastic Poisson processes) allows to model such situations. The
random intensity then writes $\lambda(t)=\theta(t,Z_t)$ where $\theta$ is a
non-random function, $t\in\mathbb{R}^+$ is the time variable and
$(Z_t)_{t\in\mathbb{R}^+}$ is the $d$-dimensional covariates process. For a
longitudinal study over $n$ patients, we observe
$(N_t^k,Z_t^k)_{t\in\mathbb{R}^+}$ for $k=1,\ldots,n$. The intention is to
estimate the intensity of the process using these observations and to study the
properties of this estimator.
