Coursebooks

Probability theory

MATH-432

Lecturer(s) :

Chong Carsten Hao Ye

Language:

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:

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.

Ressources en bibliothèque
Websites

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

Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14 MED 2 1522
14-15
15-16 MED 2 1522
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