Stochastic Partial Differential Equations
The first half of the course is devoted to explaining fundamental concepts, terms, facts and tools in probability theory and stochastic analysis. Then, in the second half, we discuss the stochastic partial differential equations as applications of stochastic analysis.
讲师
日期
2023年09月26日 至 12月26日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 09:50 - 11:25 | A3-3-301 | ZOOM 03 | 242 742 6089 | BIMSA |
修课要求
It is desirable that the audience is familiar with modern probability theory and some tools in stochastic analysis. But I will try to briefly explain these in my course.
课程大纲
The course consists of the following two parts.
(1) Foundations of Probability Theory and Stochastic Analysis:
Probability space, Convergence of random variables, Independence, Conditional probability, Strong law of large numbers, Kolmogorov's inequality, Convergence in law, Central limit theorem, Discrete and continuous time martingales, Brownian motion, Stochastic integrals, Ito's formula, Stochastic differential equations, Relation to partial differential equations
(2) Stochastic Partial Differential Equations:
Stochastic Allen-Cahn equation, Time-dependent Ginzburg-Landau equation, Singular stochastic partial differential equations, KPZ (Kardar-Parisi-Zhang) equation, coupled KPZ equation
(1) Foundations of Probability Theory and Stochastic Analysis:
Probability space, Convergence of random variables, Independence, Conditional probability, Strong law of large numbers, Kolmogorov's inequality, Convergence in law, Central limit theorem, Discrete and continuous time martingales, Brownian motion, Stochastic integrals, Ito's formula, Stochastic differential equations, Relation to partial differential equations
(2) Stochastic Partial Differential Equations:
Stochastic Allen-Cahn equation, Time-dependent Ginzburg-Landau equation, Singular stochastic partial differential equations, KPZ (Kardar-Parisi-Zhang) equation, coupled KPZ equation
参考资料
[1] D. Williams: Probability with Martingales, Cambridge, 1991.
[2] J-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer, 2013.
[3] I. Karatzas and S.E. Shreve: Brownian Motion and Stochastic Calculus, Springer, 1991.
[4] T. Funaki, Lectures on Random Interfaces (Chapters 3, 4, 5), SpringerBriefs, 2016.
[5] Slides and Videos of Funaki's courses at Yau center: 2022, 2020
https://ymsc.tsinghua.edu.cn/en/info/1050/1967.htm
https://ymsc.tsinghua.edu.cn/en/info/1051/1518.htm
[2] J-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer, 2013.
[3] I. Karatzas and S.E. Shreve: Brownian Motion and Stochastic Calculus, Springer, 1991.
[4] T. Funaki, Lectures on Random Interfaces (Chapters 3, 4, 5), SpringerBriefs, 2016.
[5] Slides and Videos of Funaki's courses at Yau center: 2022, 2020
https://ymsc.tsinghua.edu.cn/en/info/1050/1967.htm
https://ymsc.tsinghua.edu.cn/en/info/1051/1518.htm
听众
Undergraduate
, Graduate
视频公开
不公开
笔记公开
不公开
语言
英文
讲师介绍
Funaki Tadahisa曾任东京大学教授，后任早稻田大学教授，2022年加入北京雁栖湖应用数学研究院任研究员。2007年获得日本数学会秋季奖，2022年国际数学家大会受邀报告人，曾担任日本数学会理事长。他的主要研究与统计物理学有关概率论，特别是相互作用系统和随机偏微分方程，而随着几个菲尔兹奖被授予这些领域，其重要性也在逐步增加。