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Singular reflected diffusions

Sayan Banerjee, University of North Carolina, Chapel Hill
Monday, February 25, 2019 - 2:30pm to 3:20pm
DEM 126

I will talk about some models coming from Statistical Physics and Queueing Theory that give rise to singular reflected processes in their diffusion limit. Such diffusions are characterized by non-elliptic generators (which are not even hypoelliptic) in the interior, and ergodicity arises from non-trivial interactions between the diffusion, drift and reflection. I will talk about a regenerative process approach which identifies renewal times in diffusion paths and analyzes excursions between successive renewal times. This provides a detailed description of the stationary distribution even when closed form expressions are unavailable.

Based on joint works with Chris Burdzy, Brendan Brown, Mauricio Duarte and Debankur Mukherjee.

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