Article Dans Une Revue Stochastic Processes and their Applications Année : 2024

Sticky diffusions on star graphs : characterization and Itô formula

Résumé

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 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.

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Dates et versions

hal-04772414 , version 1 (07-11-2024)
hal-04772414 , version 2 (03-06-2025)
hal-04772414 , version 3 (17-10-2025)

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Jules Berry, Fausto Colantoni. Sticky diffusions on star graphs : characterization and Itô formula. Stochastic Processes and their Applications, In press, ⟨10.1016/j.spa.2025.104795⟩. ⟨hal-04772414v3⟩
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