Markovian bridges: Weak continuity and pathwise constructions

Details Markovian bridges: Weak continuity and pathwise constructions Markovian bridges: Weak continuity and pathwise constructions

2009-05-13

arxiv.org/abs/0905.2155v3

Annals of Probability 2011, Vol. 39, No. 2, 609-647

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AOP562 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/10-AOP562

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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