Geodesic
Asymptotic properties of an intensity estimator of an inhomogeneous Poisson process in a combined model
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 2, pp. 351-372 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, maximal likelihood estimate, consistency, asymptotic normality, Sobolev space.
Mots-clés : diffusion 
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     author = {A. G. Kukush and Yu. S. Mishura},
     title = {Asymptotic properties of an intensity estimator of an inhomogeneous {Poisson} process in a combined model},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {351--372},
     year = {1999},
     volume = {44},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_2_a5/}
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A. G. Kukush; Yu. S. Mishura. Asymptotic properties of an intensity estimator of an inhomogeneous Poisson process in a combined model. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 2, pp. 351-372. http://geodesic.mathdoc.fr/item/TVP_1999_44_2_a5/