Brownian motion

Reflected Brownian motion

Physics

Mathematics

Knowledge management

Boundary (topology)

Geometric Brownian motion

Statistical physics

Statistics

Limit (mathematics)

Mathematical analysis

Markov process

Computer science

Quantum mechanics

Innovation diffusion

Observable

Diffusion process

Large deviations theory

Physical review. E

We study the large deviations of time-integrated observables of Markov diffusions that have perfectly reflecting boundaries. We discuss how the standard spectral approach to dynamical large deviations must be modified to account for such boundaries by imposing zero-current conditions, leading to Neumann or Robin boundary conditions, and how these conditions affect the driven process, which describes how large deviations arise in the long-time limit. The results are illustrated with the drifted Brownian motion and the Ornstein-Uhlenbeck process reflected at the origin. Other types of boundaries and applications are discussed.

Dynamical large deviations of reflected diffusions