In this talk, I will first present main ideas of recent results of the ergodicity of random periodic processes. They include random periodic paths, periodic measures, their “equivalence”, their lifts, construction of invariant measures, ergodicity and spectral characteristics. Then I will present random quasi-periodic processes, quasi-periodic measures and lifted invariant measure and ergodicity. Application to concrete SDEs such as stochastic resonance model of Benzi, Parisi, Stera and Vulpiani will also be given.
This talk is based on a series of joint work with Chunrong Feng, Yu Liu, Yujia Liu, Baoyou Qu and Johnny Zhong.
会议网址:https://kansas.zoom.com.cn/j/99492418370
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赵怀忠,1984年毕业于山东大学数学系数学专业,1990年在中国科学院应用数学所获得博士学位(动力系统),1995年取得英国华威大学数学研究所博士学位(随机分析)。早期曾在中科院应用数学研究所、意大利国际理论物理中心(ICTP)、英国斯旺西大学、美国加利福尼亚大学尔湾分校任职,1999年到英国拉夫堡大学,2007年晋升为教授,现为英国杜伦大学教授,山东大学高层次人才特聘教授。曾入选英国工程与物理科学学部基金委资深人才计划(EPSRC Established Career Fellowship)、国家海外高层次人才。先后在 Mem. Amer. Math. Soc.、 Comm. Math. Phys.、 J. Funct. Anal.、 J. Differential Equations、 Stochastic Process. Appl.、SIAM J. Control Optim.、 SIAM J. Numer. Anal.、Nonlinearity、Phys. D 等期刊上发表论文70余篇。主要研究方向为随机分析,涉及随机微分方程/随机偏微分方程、非线性期望,特别是随机动力学、遍历性理论等。已成功培养21人获博士学位,16位博士后,1位牛顿高级学者。