Representations of multidimensional linear process bridges

Matyas Barczy; Peter Kern

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arXiv · 1011.0067

Representations of multidimensional linear process bridges

Matyas Barczy·Peter Kern

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Abstract

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.

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Matyas Barczy, Peter Kern. 2010-10-30. Representations of multidimensional linear process bridges. https://arxiv.org/abs/1011.0067

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