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Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity

Menshikov, Mikhail V.; Mijatović, Aleksandar; Wade, Andrew R.

Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity Thumbnail


Authors

Aleksandar Mijatović



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.

Citation

Menshikov, M. V., Mijatović, A., & Wade, A. R. (2023). Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 59(4), 1813-1843. https://doi.org/10.1214/22-AIHP1309

Journal Article Type Article
Acceptance Date Aug 26, 2022
Publication Date 2023-11
Deposit Date Mar 3, 2022
Publicly Available Date Nov 30, 2023
Journal Annales de l'Institut Henri Poincaré
Print ISSN 0246-0203
Publisher Institute of Mathematical Statistics
Peer Reviewed Peer Reviewed
Volume 59
Issue 4
Pages 1813-1843
DOI https://doi.org/10.1214/22-AIHP1309
Public URL https://durham-repository.worktribe.com/output/1212811

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