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

Author

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  • Hatem Hajri

    (Institut VEDECOM)

  • Marc Arnaudon

    (Institut de Mathématiques de Bordeaux UMR 5251)

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.

Suggested Citation

  • Hatem Hajri & Marc Arnaudon, 2019. "On a Coupling of Solutions to the Interface Stochastic Differential Equation on a Star Graph," Journal of Theoretical Probability, Springer, vol. 32(1), pages 90-105, March.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:1:d:10.1007_s10959-017-0803-z
    DOI: 10.1007/s10959-017-0803-z
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    References listed on IDEAS

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    1. Hajri, Hatem & Raimond, Olivier, 2016. "Stochastic flows and an interface SDE on metric graphs," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 33-65.
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