Prevalence of heavy-tailed distributions in systems with multiple scales: insights through stochastic averaging

Series: 
Stochastics Seminar
Thursday, November 29, 2018 - 3:05pm
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
School of Mathematics, GaTech
Organizer: 
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).