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Reflected Brownian motion in generalised parabolic domains
This talk will describe the long-time behaviour of driftless reflected diffusions in unbounded domains of generalised parabolic type. Asymptotically normal reflection leads to the reflected diffusion exhibiting phenomena ranging from transience to polynomial ergodicity. If the reflection is asymptotically oblique, there is a natural dichotomy according to whether it is pointing “away from” (—>) or “towards” (<—) the origin. In the case (—>), we characterise explosion and almost sure superdiffusivity of the process, including a second-order CLT-type result in the superdiffusive case. In the case (<—), we characterise phenomena ranging from sub-exponential to uniform ergodicity. In the uniformly ergodic case, the reflected process can be started from infinity (with an “infinite amount” of local time at time zero). All of the criteria for these stochastic phenomena are in terms of the asymptotic behaviour at infinity of the model parameters. This is joint work with Miha Bresar, Juan Pablo Chavez Ochoa, Mikhail Menshikov, Isao Sauzedde and Andrew Wade.
Date:
26 January 2026, 14:00
Venue:
Mathematical Institute, Woodstock Road OX2 6GG
Venue Details:
L5
Speaker:
Aleks Mijatović (University of Warwick)
Organising department:
Department of Statistics
Organisers:
Matthias Winkel (Department of Statistics, University of Oxford),
Julien Berestycki (University of Oxford),
Christina Goldschmidt (Department of Statistics, University of Oxford),
James Martin (Department of Statistics, University of Oxford)
Part of:
Probability seminar
Booking required?:
Not required
Audience:
Public
Editor:
Christina Goldschmidt
