We define a generalized Brownian bridge and we provide some information about its filtration. Two decompositions of this process as a semi-martingale are given. The first one is a Volterra decomposition and the second one is its canonical decomposition in its own filtration.
"Canonical Decompositions of Certain Generalized Brownian Bridges." Electron. Commun. Probab. 7 27 - 35, 2002. https://doi.org/10.1214/ECP.v7-1044