Event description
I will present the construction of some stochastic processes in a star graph, that is a non-euclidean structure where some features of the classical modelling fail.
In particular, I will define Brownian motions on graphs and how to construct them.
Based on this construction, I will discuss sticky behaviour in the vertex of the graph, first in the Markovian framework, then in a more general setting.
We shall first discuss the diffusion property of the sticky Brownian motion;
then, we introduce a parabolic problem on the star graph with non-local dynamic conditions in the vertex.
Extensions to general graph structures can be given by applying to our results a localisation technique.
This is based on joint works with Mirko D’Ovidio and Fausto Colantoni (Sapienza University, Rome, Italy).