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Asymptotic Distributions for the Ornstein-Uhlenbeck Process

✍ Scribed by John A. Beekman

Book ID
111698202
Publisher
Applied Probability Trust
Year
1975
Tongue
English
Weight
577 KB
Volume
12
Category
Article
ISSN
0021-9002

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Let x(t) be an Ornstein-Uhlenbeck process and y(t) a diffusion process. Formulae are obtained for the characteristic and probability density functions of x(T(y)), where T(y) is the first passage time of y(t) to the boundary y(t) --d, starting from y.

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It is shown that the suitably normalized maximum likelihood estimators of some parameters of multidimensional Ornstein Uhlenbeck processes with coefficient matrix of a special structure have exactly a normal distribution. This result provides a generalization to an arbitrary dimension of the well-kn