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Abstract.
We derive bridges from general multidimensional linear non time-homogeneous processes by using only the transition densities of the original process giving their integral representations (in terms of a standard Wiener process) and their so-called anticipative representations. We derive a stochastic differential equation satisfied by the integral representation and we prove a usual conditioning property for general multidimensional linear process bridges. We specialize our results for the one-dimensional case; especially, we study one-dimensional Ornstein–Uhlenbeck bridges.
Keywords: Linear process bridge; Markov transition densities; h-transform; integral representation; anticipative representation; Ornstein–Uhlenbeck bridge
Received: 2012-01-25
Revised: 2013-03-06
Accepted: 2013-04-06
Published Online: 2013-06-05
Published in Print: 2013-06-01
© 2013 by Walter de Gruyter Berlin Boston
