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March 2011 Markovian bridges: Weak continuity and pathwise constructions
Loïc Chaumont, Gerónimo Uribe Bravo
Ann. Probab. 39(2): 609-647 (March 2011). DOI: 10.1214/10-AOP562

Abstract

A Markovian bridge is a probability measure taken from a disintegration of the law of an initial part of the path of a Markov process given its terminal value. As such, Markovian bridges admit a natural parameterization in terms of the state space of the process. In the context of Feller processes with continuous transition densities, we construct by weak convergence considerations the only versions of Markovian bridges which are weakly continuous with respect to their parameter. We use this weakly continuous construction to provide an extension of the strong Markov property in which the flow of time is reversed. In the context of self-similar Feller process, the last result is shown to be useful in the construction of Markovian bridges out of the trajectories of the original process.

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Loïc Chaumont. Gerónimo Uribe Bravo. "Markovian bridges: Weak continuity and pathwise constructions." Ann. Probab. 39 (2) 609 - 647, March 2011. https://doi.org/10.1214/10-AOP562

Information

Published: March 2011
First available in Project Euclid: 25 February 2011

zbMATH: 1217.60066
MathSciNet: MR2789508
Digital Object Identifier: 10.1214/10-AOP562

Subjects:
Primary: 60J25
Secondary: 60J65

Keywords: Markov bridges , Markov self-similar processes

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 2 • March 2011
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