|Title||Properties of the Ornstein-Uhlenbeck bridge|
|Publication Type||Journal Article|
|Year of Publication||2013|
This note is a study of the Ornstein-Uhlenbeck bridge and its main properties. We present the derivation of its canonical decomposition in the ﬁrst section of the paper using ﬁltration enlargement techniques. In the second section, we present its Karhunen-Loève expansion, for any value of the initial variance and mean-reversion parameter (or mean-repulsion if negative). In the third section, we present an application to the optimal functional quantization of the Ornstein-Uhlenbeck bridge.