Description
Department Colloquium.
Speaker: Rachel Kuske.
Affiliation: Georgia Tech.
Date and Time: Wednesday 03 April, 4:00 pm - 5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Prevalence of heavy-tailed distributions in systems with multiple
scales: insights through stochastic averaging.
Abstract: Heavy tailed distributions have been shown to be consistent with
data in a variety of systems with multiple time scales. Recently,
increasing attention has appeared in different phenomena related to
climate. For example, correlated additive and multiplicative (CAM)
Gaussian noise, with infinite variance or heavy tails in certain parameter
regimes, has received increased attention in the context of atmosphere
and ocean dynamics. We discuss how CAM noise can appear generically in
many reduced models. Then we show how reduced models for systems driven by
fast linear CAM noise processes can be connected with the stochastic
averaging for multiple scales systems driven by alpha-stable processes. We
identify the conditions under which the approximation of a CAM noise
process is valid in the averaged system, and illustrate methods using
effectively equivalent fast, infinite-variance processes. These
applications motivate new stochastic averaging results for systems with
fast processes driven by heavy-tailed noise. We develop these results for
the case of alpha-stable noise, and discuss open problems for identifying
appropriate heavy tailed distributions for these multiple scale systems.
This is joint work with Prof. Adam Monahan (U Victoria) and Dr. Will
Thompson (UBC/NMi Metrology and Gaming).