Analytic and stochastic description of Brownian motions on star-like graphs (Andrey Pilipenko, UNIGE)

13.10.2025 16:15 – 18:00

Abstract:
Let S be a star-like graph, which is a union of finite number of rays with a common vertex 0. We provide a complete description of all Feller processes on S that behave like a Brownian motion on each ray until hitting 0. These processes are described from both an analytical and a stochastic point of view. The description includes:
(a) the construction of Markov semigroup generators on S with Wenzell-Feller boundary conditions at 0, which describe a mixture of reflection, killing, time delay, and jump exit at 0 with possibly infinite intensity, as well as the calculation of the explicit form of the resolvent of the process;
(b) representation of the process as a measurable function of finite number of Wiener processes and subordinators.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire Math Physics

entrée libre