Sticky diffusions on star graphs : characterization and It{\^o} formula

TL;DR

This paper characterizes sticky diffusions on star graphs, providing an Itô formula and stochastic differential equations, extending known results from simpler structures to more complex graph configurations.

Contribution

It introduces a novel characterization of sticky diffusions on star graphs as time-changed nonsticky diffusions and establishes an Itô formula for these processes.

Findings

Characterization of sticky diffusions as time-changed nonsticky diffusions

Derivation of an Itô (Freidlin-Sheu) formula for sticky diffusions on star graphs

Stochastic differential equation for the radial component of the process

Abstract

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 It{\^o} and McKean. We prove a form of It{\^o} 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.