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Zbl 0566.62070
Kutoyants, Yu.A.
Parameter estimation for diffusion type processes of observation. (English)
[J] Math. Operationsforsch. Stat., Ser. Stat. 15, 541-551 (1984). ISSN 0323-3944

The asymptotic properties of the maximum likelihood and Bayesian estimates of the trend coefficient of a diffusion type process are investigated. General conditions are given which assure uniform consistency, asymptotic normality, convergence of moments and asymptotic efficiency of these estimates. \par The conditions allow for three types of limits: the observation period tends to infinity, the trend coefficient tends to infinity, the diffusion coefficient tends to zero, or any combination of these. The proofs are partly based on former work of the author and on the work of Ibragimov, Hasminski and others. Additionally, some examples are given.
[L.Fahrmeir]

MSC 2000:: *62M05 Markov processes: estimation
62F12 Asymptotic properties of parametric estimators

Keywords: maximum likelihood; Bayesian estimates; trend coefficient; diffusion type process; uniform consistency; asymptotic normality; convergence of moments; asymptotic efficiency; observation period; diffusion coefficient

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