Probabilistic approximations, spring 2015
Probabilistic approximations, spring 2015
Lecturer
Ehsan Azmoodeh, University of Luxembourg
Scope
3 sp.
Type
Advanced studies
Prerequisites
A basic knowledge about probability theory in the level of the book Probability Essentials by Jean Jacod and Philip Protter. Some knowledge about Malliavin calculus will help a lot, but it is not necessary, the essential ingredients from Malliavin Calculus will be discussed in the lectures.
Content
The aim of the course is to combine two probabilistic techniques, namely the Malliavin calculus and Stein's method to study the Gaussian and non-Gaussian approximations of non-linear functionals of infinite-dimensional Gaussian fields. One of the main objectives of the course is to prove an interesting result in modern theory of probabilistic approximations known nowadays as the fourth moment theorem.
Lectures
On mondays March 23, April 27 and May 25 at 12-14 in room CK107,
on thursdays March 26 at 15-17, April 30 at 14-16 and May 28 at 15-17 in room C129
Exercise classes
On friday March 27 at 10-12 in room B321, on Thursday April 30 at 12-14 in B321, and on wednesday May 27 at 10-12 in B322.
(27.3) (30.4) (29.5)
Exams
To pass the course, students have to solve the exercises assigned during each week and to write an home exam at the end of the cycle of lectures.
Bibliography
Book: Nourdin Ivan, Peccati Giovanni: Normal Approximations with Malliavin Calculus: From Stein's Method to Universality. Cambridge Tracts in Mathematics, 2012.
Registration
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