Stochastic Partial Differential Equations II
This course is a continuation of my course in the last semester. We continue our discussion on the semilinear stochastic partial differential equations (SPDEs) of parabolic type. Then we discuss the quasilinear SPDEs, singular SPDEs and some applications of SPDEs.
Lecturer
Date
27th February ~ 23rd May, 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
Undergraduate
, Graduate
Video Public
No
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.