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.
Lecturer
Date
10th September ~ 10th December, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Tuesday,Thursday | 09:50 - 11:25 | A3-3-301 | ZOOM 05 | 293 812 9202 | BIMSA |
Prerequisite
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.
Syllabus
(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.
Reference
[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.
Audience
Advanced Undergraduate
, Graduate
Video Public
Yes
Notes Public
No
Language
English
Lecturer Intro
Funaki Tadahisa was a professor at University of Tokyo (1995-2017) and at Waseda University (2017-2022) in Japan. His research subject is probability theory mostly related to statistical physics, specifically interacting systems and stochastic PDEs. He was a president of Mathematical Society of Japan (2013-2015), and was an invited sectional lecturer at ICM 2022.