Maximum likelihood estimation for a Poisson process of discontinuous intensity

We consider the problem of maximum likelihood estimation of a parameter from n independent observations of inhomogeneous Poisson process of discontinuous intensity. The unknown parameter is two dimensional and its first component is the amplitude and the second one is the frequency. We show that the estimator of the amplitude is asymptotically normal with the rate root n and the estimator of the frequency converges to a nondegenerate limiting distribution with the rate n. (C) 1999 Academie des Sciences / Editions scientifiques et medicales Elsevier SAS.