The Annals of Probability

Markovian bridges: Weak continuity and pathwise constructions

Loïc Chaumont and Gerónimo Uribe Bravo

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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.

Article information

Source
Ann. Probab., Volume 39, Number 2 (2011), 609-647.

Dates
First available in Project Euclid: 25 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.aop/1298669175

Digital Object Identifier
doi:10.1214/10-AOP562

Mathematical Reviews number (MathSciNet)
MR2789508

Zentralblatt MATH identifier
1217.60066

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60J65: Brownian motion [See also 58J65]

Keywords
Markov bridges Markov self-similar processes

Citation

Chaumont, Loïc; Uribe Bravo, Gerónimo. Markovian bridges: Weak continuity and pathwise constructions. Ann. Probab. 39 (2011), no. 2, 609--647. doi:10.1214/10-AOP562. https://projecteuclid.org/euclid.aop/1298669175


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