Work

Central limit theorem for superdiffusive reflected Brownian motion

Year: 2026

Type: article

Abstract: We study the second-order asymptotics around the superdiffusive strong law (Ann. Inst. Henri Poincaré Probab. Stat. 59 (2023) 1813–1843) of a multidimensional driftless diffusion with oblique reflection from the boundary in a generalised parabolic domain. In the unbounded direction we prove the limit is Gaussian with the usual diffusive scaling, while in the appropriately scaled cross-sectional slice we establish convergence to the invariant law of a reflecting diffusion in a unit ball. Using the separation of time scales, we also show asymptotic independence between these two components. The parameters of the limit laws are explicit in the growth rate of the boundary and the asymptotic diffusion matrix and reflection vector field. A phase transition occurs when the domain becomes too narrow, in which case we prove that the central limit theorem for the unbounded component fails.

Source: The Annals of Applied Probability

DOI: 10.1214/25-aap2272

Authors: Aleksandar Mijatović, Isao Sauzedde, Andrew Wade

Institutions: University of Warwick, Durham University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Awards: Isaac Newton Institute for Mathematical Sciences (INI), G2596867474, Anomalous diffusion via self-interaction and reflection, Anomalous diffusion via self-interaction and reflection, DMS-EPSRC: Fast martingales, large deviations and randomised gradients for heavy-tailed target distributions