Properties of the Ornstein-Uhlenbeck bridge

Abstract: This paper presents a study of the properties of the Ornstein-Uhlenbeck bridge, specifically, we derive its Karhunen-Lo`eve expansion for any value of the initial variance and mean-reversion parameter (or mean-repulsion if negative). We also show that its canonical decomposition can be obtained using some techniques related to generalized bridges. Finally, we present an application to the optimal functional quantization of the Ornstein-Uhlenbeck bridge.