Stochastic flows on metric graphs
Hatem Hajri, Olivier Raimond (UP10)
TL;DR
This paper investigates stochastic differential equations on metric graphs, characterizing the laws of solutions and extending previous work to more general graph structures.
Contribution
It generalizes the understanding of stochastic flows on metric graphs beyond specific cases, providing a broader theoretical framework.
Findings
Describes the laws of solutions under certain conditions
Extends previous results to general oriented metric graphs
Provides a foundation for future studies on stochastic flows on complex graphs
Abstract
We study a simple stochastic differential equation driven by one Brownian motion on a general oriented metric graph whose solutions are stochastic flows of kernels. Under some condition, we describe the laws of all solutions. This work is a natural continuation of some previous papers by Hajri, Hajri-Raimond and Le Jan-Raimond where some particular graphs have been considered.
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