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Pré-Publication, Document De Travail Année : 2017

On a coupling of solutions to the interface SDE on a star graph

To appear in Journal of Theoretical Probability

Résumé

Inspired by Tsirelson proof of the non Brownian character of Walsh Brownian motion ltration on three or more rays, we prove some results on a particular coupling of solutions to the interface SDE on a star graph, recently introduced. This coupling consists in two solutions which are independent given the driving Brownian motion. As a consequence, we deduce that if the star graph contains 3 or more rays, the argument of the solution at a xed time is independent of the driving Brownian motion.
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Dates et versions

hal-01262654 , version 1 (27-01-2016)
hal-01262654 , version 2 (24-03-2016)
hal-01262654 , version 3 (12-12-2017)

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Hatem Hajri, Marc Arnaudon. On a coupling of solutions to the interface SDE on a star graph . 2017. ⟨hal-01262654v3⟩
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