On a Coupling of Solutions to the Interface Stochastic Differential Equation on a Star Graph

Hatem Hajri () and Marc Arnaudon ()
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Hatem Hajri: Institut VEDECOM
Marc Arnaudon: Institut de Mathématiques de Bordeaux UMR 5251

Journal of Theoretical Probability, 2019, vol. 32, issue 1, 90-105

Abstract: Abstract Inspired by Tsirelson’s proof of the non-Brownian character of Walsh Brownian motion filtration on three or more rays, we prove some results on a particular coupling of solutions to the interface stochastic differential equation on a star graph, recently introduced in Hajri and Raimond (Stoch Process Appl 126:33–65, 2016). This coupling consists of two solutions which are independent given the driving Brownian motion. As a consequence, we deduce that if the star graph contains three or more rays, the argument of the solution at a fixed time is independent of the driving Brownian motion.

Keywords: Tsirelson theorem; Non-Brownian filtration; Walsh Brownian motion; Stochastic equations on graphs; 60H05; 60H10; 60J25; 60G48 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-017-0803-z

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