This article is cited in 1 paper

Asymptotic properties of an intensity estimator of an inhomogeneous Poisson process in a combined model

A. G. Kukush, Yu. S. Mishura

National Taras Shevchenko University of Kyiv, Faculty of Mechanics and Mathematics

Abstract: A stochastic process with a drift, a diffusion, and a Poisson component is considered, where the last is an inhomogeneous process with unknown intensity $\lambda=\lambda(t)$ belonging to a compact of a Sobolev space. By observations over the process within a time interval $[0,T]$ we construct the maximum likelihood estimator (MLE) of $\lambda$. Conditions providing consistency of the estimator and asymptotic normality of the functionals of it are studied. A comparison is given of the MLEs constructed by the observations over the whole process and over its individual components.

Keywords: inhomogeneous Poisson process, intensity, drift, diffusion, maximal likelihood estimate, consistency, asymptotic normality, Sobolev space.

Received: 14.06.1996

DOI: 10.4213/tvp770

 English version: Theory of Probability and its Applications, 2000, 44:2, 273–292

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