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Parameter estimation for diffusion type processes of observation. (English) Zbl 0566.62070

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.

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.

Reviewer: L.Fahrmeir
MSC:
62M05Markov processes: estimation
62F12Asymptotic properties of parametric estimators