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Application of stochastic flows to the interface SDE on a star graph

Research paper by Hatem Hajri, Marc Arnaudon

Indexed on: 24 Mar '16Published on: 24 Mar '16Published in: Mathematics - Probability



Abstract

Using a perturbation method of stochastic flows of kernels, we prove some results on a particular coupling of solutions to the interface SDE on a star graph. 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 fixed time is independent of the driving Brownian motion.