Bridges with Random Length: Gaussian-Markovian Case

#### M. Erraoui, M. Louriki

2018, v.24, Issue 4, 669-693

ABSTRACT

Motivated by the Brownian bridge on random interval considered by Bedini et al \cite{BBE}, we introduce and study Gaussian bridges with random length with special emphasis to the Markov property. We prove that if the starting process is Markov then this property is kept by the bridge with respect to the usual augmentation of its natural filtration. This leads us to conclude that the completed natural filtration of the bridge satisfies the usual conditions of right-continuity and completeness.
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Keywords: Gausssian process, Gaussian bridge, Markov process, Bayes theorem