Stochastic Analysis and its Applications

Speaker:Prof. Tadahisa Funaki (University of Tokyo)
Schedule:Tuesdays, Fridays, 11:30am-1:00pm, 2022-3-8~2022-6-10 (no lecture on May 3)
Venue:Zoom Meeting ID: 849 963 1368 Passcode: YMSC

Note: There is no lecture on May 3, 2022 for it's Labor Day Holiday.


Abstract:

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 pick up some topics in stochastic partial differential equations as applications of stochastic analysis.

Contents:

(1) Foundations of Probability Theory (5 lectures)

Probability space, Dynkin's pi-lambda theorem, Convergence of random variables, Independence, Conditional probability, Strong law of large numbers, Kolmogorov's inequality, Convergence in law, Central limit theorem

 

(2) Foundations of Stochastic Analysis (9 lectures)

Discrete and continuous time martingales, Brownian motion, Stochastic integrals, Ito's formula, Stochastic differential equations, Relation to PDEs

 

(3) Applications of Stochastic Analysis (14 lectures)

Stochastic partial differential equations, Random interfaces, (Stochastic) Motion by mean curvature, Stochastic Allen-Cahn equation, Time-dependent Ginzburg-Landau equation, Other topics.

 

References:

T. Funaki, Lectures on Random Interfaces, SpringerBriefs, 2016.

I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics, 113, Springer, 2nd edition, 1991.


Course Slides: 

  Lect-1.pdf Lect-2.pdf Lect-3.pdf  Lect-4.pdf  Lect-5.pdf  Lect-6.pdf  Lect-7.pdf  Lect-8.pdf  Lect-9.pdf  Lect-10.pdf

 Lect-11.pdf  Lect-12.pdf  Lect-13.pdf  Lect-14.pdf  Lect-15.pdf  Lect-16.pdf  Lect-17.pdf   Lect-18.pdf   Lect-19.pdf   Lect-20.pdf   Lect-21.pdf   Lect-22.pdf   Lect-23.pdf   Lect-24.pdf   Lect-25.pdf   Lect-26.pdf   Lect-27.pdf

 

 

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Lecture23-27:

http://archive.ymsc.tsinghua.edu.cn/pacm_course?html=Stochastic_Analysis_and_its_Applications.html