Properties of the Ornstein-Uhlenbeck bridge

Sylvain Corlay (1)

1 Bloomberg L.P. Quantitative Finance Research

This paper is a study of the properties of the Ornstein-Uhlenbeck bridge. We derive its canonical decomposition using filtration enlargement techniques, and its Karhunen-Loève expansion for any value of the initial variance and mean-reversion parameter (or mean-repulsion if negative). Finally, we present an application to the optimal functional quantization of the Ornstein-Uhlenbeck bridge.

Mots clés: Ornstein-Uhlenbeck bridge; canonical decomposition; Karhunen-Loève; filtration enlargement; functional quantization

Domaines: Probabilités [math.PR]

Sylvain Corlay. Properties of the Ornstein-Uhlenbeck bridge. 2013. ⟨hal-00875342v3⟩