Properties of the Ornstein-Uhlenbeck bridge

Understand

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.