Title: Stochastic averaging for multiple scale models driven by fat-tailed noise
Speaker: Rachel Kuske (Geogia Tech)
Abstract: Stochastic averaging has a long history for systems with multiple time scales and Gaussian forcing, but far less attention has been paid to problems where the stochastic forcing has infinite variance, such as in Levy processes or alpha-stable noise. Correlated additive and multiplicative (CAM) Gaussian noise, with infinite variance or ``fat tails’’ in certain parameter regimes, can arise generically in many models with parametric uncertainty and has received increased attention in the context of atmosphere and ocean dynamics. These applications motivate new reduced models using stochastic averaging for systems with fast processes driven by noise with fat tails. We develop these results for the case of alpha-stable noise, giving explicit results that use the Marcus interpretation, the infinite variance analog to the Stratonovich interpretation. 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 new types of approximations open the door for stochastic averaging in a wider range of stochastic systems with multiple time scales.
This is joint work with Prof. Adam Monahan (U Victoria) and Dr. Will Thompson (UBC/NMi Metrology and Gaming)
Biosketch: Rachel Kuske is a Professor of Mathematics at Georgia Institute of Technology, where she is also department chair. Most recently her research is in new areas of interest in stochastic dynamics, including stochastic analysis in delayed or non-smooth systems, noise-driven order in complex systems, and analysis of stochastic transitions or "tipping points" in the diverse fields of optics, biology, mechanics, and climate systems.
Before joining Georgia Tech, she was at the University of British Columbia (UBC) for 15 years, where she was elected SIAM Fellow in 2015, and received a number of other awards including a Canada Research Chair (2002-2012) and the Canadian Mathematical Society’s Krieger-Nelson prize (2011). At UBC she also held positions as Department Head (2007-2011) and as the Senior Advisor to the Provost on Women Faculty ((2011-2015). In 2016 she held a Simons Fellowship at the Newton Institute in Cambridge.
Seminar URL: https://web.math.osu.edu/colloquium/
