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Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity

Menshikov, Mikhail V. and Mijatovic, Aleksandar and Wade, Andrew R. (2022) 'Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity.', Annales de l'Institut Henri Poincaré .


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.

Item Type:Article
Full text:Publisher-imposed embargo
(AM) Accepted Manuscript
File format - PDF
Publisher Web site:
Date accepted:26 August 2022
Date deposited:26 August 2022
Date of first online publication:No date available
Date first made open access:No date available

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