Properties of the Ornstein-Uhlenbeck bridge

TitleProperties of the Ornstein-Uhlenbeck bridge
Publication TypeJournal Article
Year of Publication2013
AuthorsSylvain Corlay
JournalPreprint
Abstract

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.

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