讲座题目：Prevalence of heavy-tailed distributions in systems with multiple scales: insights through stochastic averaging 主讲人：Rachel Kuske 主持人：谈胜利 教授 开始时间：2019-07-04 13:00:00 结束时间：2019-07-04 14:00:00 讲座地址：闵行数学楼401室 主办单位：数学科学学院
报告人简介： RACHEL ANN KUSKE, Professor and Chair School of Mathematics Georgia Institute of Technology. I. EARNED DEGREES B.S. Mathematics 1987 University of Wisconsin, Green Bay, WI Ph.D. Applied Mathematics 1992 Northwestern University, Evanston, IL Ph.D. Thesis Advisor: Professor B.J. Mathowsky Ph.D. Thesis Title: Asymptotic Analysis of Random Wave Equations II. EMPLOYMENT HISTORY 2017-present Professor and Chair, School of Mathematics, Georgia Institute of Technology 2006-2016 Professor, University of British Columbia, Vancouver, BC 2011-2015 Senior Advisor to the Provost on Women Faculty, University of British Columbia, Vancouver, BC 2007-2011 Department Head, University of British Columbia, Vancouver, BC 2002-2006 Associate Professor, University of British Columbia, Vancouver, BC 2000-2002 Associate Professor, University of Minnesota, Minneapolis, Minnesota 2001-2002 Associate Director, Minnesota Center for Industrial Math, University of Minnesota, Minneapolis, Minnesota 1997-2000 Assistant Professor, University of Minnesota, Minneapolis, Minnesota 1996-1997 Assistant Professor, Tufts University, Medford, Massachusetts 1994-1996 NSF Postdoc, Stanford University, Stanford, California 1992-1993 NSF Postdoc, Stanford University, Stanford, California III. HONORS AND AWARDS 1. Harold M. Bacon Teaching Award, Stanford University, 1995 2. Sloan Dissertation Fellowship, 1991 3. Tufts University Faculty Research Summer Award, 1996 4. Tufts University Mellon Research Semester Fellowship, 1997 5. McKnight Land Grant Professorship, 1998 6. Canadian Research Chair II, Applied Math, UBC, 2002 7. Krieger-Nelson Prize, CMS, 2011 8. SIAM Fellow, 2015 9. Simons Fellowship, 2016 10. Association for Women in Mathematics Service Award, 2013 报告内容： 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). |
