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Stochastic flows and an interface SDE on metric graphs

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  • Hajri, Hatem
  • Raimond, Olivier

Abstract

This paper consists in the study of a stochastic differential equation on a metric graph, called an interface SDE (ISDE). To each edge of the graph is associated an independent white noise, which drives (ISDE) on this edge. This produces an interface at each vertex of the graph. This study is first done on star graphs with N≥2 rays. The case N=2 corresponds to the perturbed Tanaka’s equation recently studied by Prokaj (2013) and Le Jan and Raimond (2014) among others. It is proved that (ISDE) has a unique in law solution, which is a Walsh’s Brownian motion. This solution is strong if and only if N=2.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:1:p:33-65
    DOI: 10.1016/j.spa.2015.07.014
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    References listed on IDEAS

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    1. Hajri, Hatem & Touhami, Wajdi, 2014. "Itô’s formula for Walsh’s Brownian motion and applications," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 48-53.
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    Cited by:

    1. 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.

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