Work

Sticky diffusions on star graphs: Characterization and Itô formula

Year: 2025

Type: article

Abstract: In this paper, we investigate continuous diffusions on star graphs with sticky behavior at the vertex. These are Markov processes with continuous paths having a positive occupation time at the vertex. We characterize the sticky diffusions as time changed nonsticky diffusions by adapting the classical technique of Itô and McKean. We prove a form of Itô formula, also known as Freidlin-Sheu formula, for this type of process. As an intermediate step, we also obtain a stochastic differential equation satisfied by the radial component of the process. These results generalize those already known for sticky diffusions on a half-line and skew sticky diffusions on the real line.

Source: Stochastic Processes and their Applications

DOI: 10.1016/j.spa.2025.104795

Authors: Jules Berry, Fausto Colantoni

Institutions: Centre National de la Recherche Scientifique, Institut National des Sciences Appliquées de Rennes, Institut de recherche mathématique de Rennes, Université de Rennes, Sapienza University of Rome

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,520