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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.

Exercise sheet 1 (27.3) Exercise sheet 2 (30.4) Exercise sheet 3 (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

Lecture notes 1-2,  Lecture Note 3

Book: Nourdin Ivan, Peccati Giovanni: Normal Approximations with Malliavin Calculus: From Stein's Method to Universality. Cambridge Tracts in Mathematics, 2012.

 

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