Sticky diffusions on star graphs: Characterization and Itô formula

Jules Berry and Fausto Colantoni

Stochastic Processes and their Applications, 2026, vol. 192, issue C

Abstract: In this paper, we investigate continuous diffusions on star graphs with sticky behaviour 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.

Keywords: Diffusion processes; Sticky boundary conditions; Itô formula; Star graphs (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104795

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