Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity
arXiv:2203.00966 · doi:10.1214/22-AIHP1309
Abstract
For a multidimensional driftless diffusion in an unbounded, smooth, sub-linear generalized parabolic domain, with oblique reflection from the boundary, we give natural conditions under which either explosion occurs, if the domain narrows sufficiently fast at infinity, or else there is superdiffusive transience, which we quantify with a strong law of large numbers. For example, in the case of a planar domain, explosion occurs if and only if the area of the domain is finite. We develop and apply novel semimartingale criteria for studying explosions and establishing strong laws, which are of independent interest.
arXiv comment39 pages, 2 figures
References in corpus (11)
- Hybrid Atlas models
- Billiards in a general domain with random reflections
- Reflected Brownian motions in the KPZ universality class
- The heavy traffic limit of an unbalanced generalized processor sharing model
- Asymptotic behaviour of randomly reflecting billiards in unbounded tubular domains
- Limits of Multilevel TASEP and similar processes
- Rate of escape and central limit theorem for the supercritical Lamperti problem
- Integral expression for the stationary distribution of reflected brownian motion in a wedge
- Transcience/recurrence for normally reflected Brownian motion in unbounded domains
- Reflecting random walks in curvilinear wedges
- Stochastic billiards with Markovian reflections in generalized parabolic domains