# Coursebooks

## Probability theory

#### Lecturer(s) :

Chong Carsten Hao Ye

English

#### Summary

The course provides a measure-theoretic introduction to probability theory.

#### Content

- Reminder of probability spaces, random variables and expectation for random variables

- L^p-spaces and inequalities, convergence in probability, almost surely and in L^p

- Independence and the Borel-Cantelli lemmas

- Weak and strong laws of large numbers and random series

- Convergence in distribution and characteristic functions

- Central limit theorem and its generalizations

#### Learning Prerequisites

##### Required courses

Analyse I/II/IV, Probabilités

##### Recommended courses

Measure and Integration

#### Learning Outcomes

By the end of the course, the student must be able to:
• Distinguish different types of convergence
• Analyze tail events via the Borel-Cantelli Lemmas
• Analyze (sums of) independent random variables
• Prove convergence in distribution

#### Teaching methods

Ex cathedra lecture and exercises in the classroom

#### Assessment methods

Exam written

Dans le cas de l¿art. 3 al. 5 du Règlement de section, l¿enseignant décide de la forme de l¿examen qu¿il communique aux étudiants concernés.

#### Supervision

 Office hours No Assistants No Forum No

#### Resources

##### Bibliography

R. Durrett. Probability: theory and examples.

#### Prerequisite for

Probabilities, Stochastic process

### In the programs

• Mathematics - master program, 2019-2020, Master semester 1
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Probability theory
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics - master program, 2019-2020, Master semester 3
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Probability theory
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 1
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Probability theory
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2019-2020, Master semester 3
• Semester
Fall
• Exam form
Written
• Credits
5
• Subject examined
Probability theory
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14 MED21522
14-15
15-16 MED21522
16-17
17-18
18-19
19-20
20-21
21-22
Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German