Large deviations for sticky-reflecting Brownian motion with boundary diffusion

TL;DR

This paper establishes a large deviation principle for sticky-reflected Brownian motion with boundary diffusion, revealing a phase transition in the rate function and introducing a new optimal transport model that differentiates between interior and boundary motion.

Contribution

It provides the first large deviation analysis for this type of boundary diffusion process and introduces a novel optimal transport framework based on the intrinsic distance.

Findings

Identifies a sharp transition in the rate function depending on boundary diffusion speed.

Derives a new intrinsic distance that influences the optimal transport model.

Connects boundary diffusion behavior with large deviation principles.

Abstract

We study a Schilder-type large deviation principle for sticky-reflected Brownian motion with boundary diffusion, both at the static and sample path level in the short-time limit. A sharp transition for the rate function occurs, depending on whether the tangential boundary diffusion is faster or slower than in the interior of the domain. The resulting intrinsic distance naturally gives rise to a novel optimal transport model, where motion and kinetic energy are treated differently in the interior and along the boundary.