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Parameter Estimation with Exact Distribution for Multidimensional Ornstein–Uhlenbeck Processes

✍ Scribed by Gyula Pap; Martien C.A. van Zuijlen

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
619 KB
Volume
59
Category
Article
ISSN
0047-259X

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✦ Synopsis

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-known behavior of the estimator of the period of a complex AR(1) process.

1996 Academic Press, Inc.

d!(t)=&#!(t) dt+dw(t),

where w(t)=w 1 (t)+iw 2 (t), t 0, is a standard complex Wiener process (i.e., w 1 (t) and w 2 (t) are independent standard real-valued Wiener processes) and #=*&i| with *>0, | # R.

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