Stochastic Mass Transport SS2021
See here (under preprints) for the script of the course
ABOUT THE EXAM: Send me an email and we can coordinate an appointment. The exam will be oral, with a preference towards 'in person' rather than online. I will give you precise instructions concerning the precautions to be taken so that we're on the safe side (concerning Covid). The emphasis of the exam is on concepts and intuitions. The chapter on Skorokhod embedding in the lecture notes is NOT part of this exam.
CHAPTER I: Optimal Transport
Here a Link to a YouTube channel created by Alexander Posch, fellow student, illustrating Wasserstein geodesics between black-and-white images. Thanks Alexander!
You may find here and here lecture notes, slides, and codes, pertaining the computational side of optimal transport as well as some machine learning applications.
Here a link to a minicourse series on Optimal Transport and Machine Learning, to be held online by the IMSI from July 6 to July 7.
Videos of the lectures on OT:
Lecture 5 Passcode: 9FM9iL^0
Lecture 6 Passcode: &0DytXkY
Lecture 7 Passcode: 7Ur7!&A%
Lecture 8 Passcode: Ok4S$P%B
Lecture 9 Passcode: v&Qn$46?
Lecture 10 Passcode: $hJ7Z**c
Lecture 11 Passcode: Da!@P8k^
Lecture 12 Passcode #l@q&W51
Lecture 13 Passcode: .CD&=1Lx
CHAPTER II: Martingale Optimal Transport
Here for the seminal paper on the subject and here for the connection with mathematical finance. Concerning stretched Brownian motion click on the following link: 'Martingale Benamou Brenier.pdf'
Videos of the lectures on Martingale OT:
Lecture 14 Passcode: BgdjyJ%5
Lecture 15 Passcode: IgKP.PK3
Lecture 16 Passcode: 1e&yx0Wn
Lecture 17 Passcode: .HWQukk6
Lecture 18 Passcode: v^raw13m
Lecture 19 Passcode: 8@nn&hWT
Lecture 20 Passcode: ^6dWb^ak
Lecture 21 (See beginning for instructions on the exam) Passcode: Nc^my0y^
Lecture 22 Passcode: &?9LTv+.
CHAPTER IV: Causal Optimal Transport and Adapted Weak Topologies
See here for the seminal article, here for connections to finance and a flavour for the continuous-time picture, and here for a deep study of topological aspects. Concerning numerics you can check here and here for brute force approaches, respectively for causal and bicausal transport, and here for a statistical perspective.
Lecture 23 Passcode: 602wRae@
Lecture 24 Passcode: 0AS!!X3S
Lecture 25 Passcode: %Ei#9ud$
Lecture 26 Passcode: #%GYlM$0
Lecture 27 Passcode: ED01k+zA