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Inspired by Tsirelson proof of the non Brownian character of WalshBrownianmotion ltration on three or more rays, we prove some results on aparticularcoupling of solutions to the interface SDE on a star graph, recentlyintroduced.This coupling consists in two solutions which are independentgiven the drivingBrownian motion. As a consequence, we deduce that if the stargraph contains 3or more rays, the argument of the solution at a xed time isindependent of thedriving Brownian motion.

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