Stochastic flows and an interface SDE on metric graphs

Hatem Hajri and Olivier Raimond

Stochastic Processes and their Applications, 2016, vol. 126, issue 1, 33-65

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.

Keywords: Stochastic flows; Reflected Brownian motion in a wedge; Walsh’s Brownian motion (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2015.07.014

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