Properties of the Ornstein-Uhlenbeck bridge

Sylvain Corlay (1)

1 Bloomberg L.P. Quantitative Finance Research

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.

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

Domaines: Probabilités [math.PR]

Sylvain Corlay. Properties of the Ornstein-Uhlenbeck bridge. 2013. ⟨hal-00875342v1⟩