Statistical analysis of the inhomogeneous telegrapher's process

We consider a problem of estimation for the telegrapher's process on the line, say X(t), driven by a Poisson process with non constant rate. It turns out that the finite-dimensional law of the process X(t) is a solution to the telegraph equation with non constant coefficients. We give the explicit law P(theta) of the process X(t) for a parametric class of intensity functions for the Poisson process. We propose an estimator for the parameter theta of P(theta) and we discuss its properties as a first attempt to apply statistics to these models.