Stochastic flows on metric graphs

Hatem Hajri (1, 2) , Olivier Raimond (2)

1 IMS - Laboratoire de l'intégration, du matériau au système
2 MODAL'X - Modélisation aléatoire de Paris X

We study a simple stochastic differential equation (SDE) driven by one Brownian motion on a general oriented metric graph whose solutions are stochastic flows of kernels. Under some conditions, we describe the laws of all solutions. This work is a natural continuation of [17, 8, 10] where some particular metric graphs were considered.

Domains: Probability [math.PR]

Hatem Hajri, Olivier Raimond. Stochastic flows on metric graphs. Electronic Journal of Probability, 2014, 19 (1-20), ⟨10.1214/EJP.v19-2773⟩. ⟨hal-01490006⟩