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On conditional Ornstein–Uhlenbeck processes

Published online by Cambridge University Press:  01 July 2016

P. Salminen
P. Salminen*
Affiliation:
Åbo Akademi
*
∗Postal address: Mathematical Institute, Åbo Akademi, SF-20500 Åbo 50, Finland.
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Abstract

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It is well known that the law of a Brownian motion started from x > 0 and conditioned never to hit 0 is identical with the law of a three-dimensional Bessel process started from x. Here we show that a similar description is valid for all linear Ornstein–Uhlenbeck Brownian motions. Further, using the same techniques, it is seen that we may construct a non-stationary Ornstein–Uhlenbeck process from a stationary one.

Keywords

EXCESSIVE TRANSFORMS
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 16 , Issue 4 , December 1984 , pp. 920 - 922
Copyright
Copyright © Applied Probability Trust 1984 

References

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