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This article is cited in 1 scientific paper (total 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
Citation:
A. G. Kukush, Yu. S. Mishura, “Asymptotic properties of an intensity estimator of an inhomogeneous Poisson process in a combined model”, Teor. Veroyatnost. i Primenen., 44:2 (1999), 351–372; Theory Probab. Appl., 44:2 (2000), 273–292
Linking options:
https://www.mathnet.ru/eng/tvp770https://doi.org/10.4213/tvp770 https://www.mathnet.ru/eng/tvp/v44/i2/p351
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Abstract page: | 487 | Full-text PDF : | 178 | First page: | 17 |
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