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Asymptotic expansions of maximum likelihood estimators for small diffusions via the theory of Malliavin-Watanabe. (English) Zbl 0767.60035

Summary: The asymptotic expansions of the probability distributions of statistics for the small diffusion are derived by means of the Malliavin calculus. From this the second order efficiency of the maximum likelihood estimator is proved.

MSC:

60F99 Limit theorems in probability theory
62F12 Asymptotic properties of parametric estimators
60H07 Stochastic calculus of variations and the Malliavin calculus
62M05 Markov processes: estimation; hidden Markov models
62E20 Asymptotic distribution theory in statistics
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