2010/10/30 by Matyas Barczy, Peter Kern · 1 citation
Mathematics · #math.PR #msc:60J25 #msc:60G15 #msc:60H10 #msc:60J35
published as Random Operators and Stochastic Equations 21 (2), 2013, 159-189 · 37 pages
arxiv created 2010/10/30 · arxiv updated 2014/03/25
We derive bridges from general multidimensional linear non time-homogeneous processes using only the transition densities of the original process giving their integral representations (in terms of a standard Wiener process) and 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.