Stochastic Partial Differential Equations III
Stochastic partial differential equation (SPDE) is one of the recent topics actively studied in the probability group and has many applications to other fields such as physics, biology, economics. The course is a continuation of that of the last semester, but being considerate of a new audience, I will recall some necessary knowledge from my last courses. Then we will continue our discussion on the semilinear SPDEs of the parabolic type, and develop it to the quasilinear SPDEs, singular SPDEs, and also touch some applications of SPDEs.
讲师
日期
2024年09月10日 至 12月10日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周二,周四 | 09:50 - 11:25 | A3-3-301 | ZOOM 05 | 293 812 9202 | BIMSA |
修课要求
It is desirable that the audience has attended my course in the last semester. But I will try to briefly recall some fundamental concepts, terms, facts and tools in modern probability theory and stochastic analysis, and also some results in SPDEs explained in the last semester.
课程大纲
(1) Foundations of Probability Theory and Stochastic Analysis
We briefly recall some fundamental concepts, terms, facts and tools explained in the last semester.
(2) Stochastic Partial Differential Equations
We discuss semilinear and quasilinear SPDEs of parabolic type, singular SPDEs, KPZ (Kardar-Parisi-Zhang) equation, coupled KPZ equation, stochastic Allen-Cahn equation, time-dependent Ginzburg-Landau equation and others.
We briefly recall some fundamental concepts, terms, facts and tools explained in the last semester.
(2) Stochastic Partial Differential Equations
We discuss semilinear and quasilinear SPDEs of parabolic type, singular SPDEs, KPZ (Kardar-Parisi-Zhang) equation, coupled KPZ equation, stochastic Allen-Cahn equation, time-dependent Ginzburg-Landau equation and others.
参考资料
[1] J-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer, 2013.
[2] I. Karatzas and S.E. Shreve: Brownian Motion and Stochastic Calculus, Springer, 1991.
[3] T. Funaki, Lectures on Random Interfaces (Chapters 3, 4, 5), SpringerBriefs, 2016.
[2] I. Karatzas and S.E. Shreve: Brownian Motion and Stochastic Calculus, Springer, 1991.
[3] T. Funaki, Lectures on Random Interfaces (Chapters 3, 4, 5), SpringerBriefs, 2016.
听众
Advanced Undergraduate
, Graduate
视频公开
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。