Sticky diffusions on star graphs: Characterization and Itô formula

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.