Fiches de cours 2018-2019

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Stochastic processes

MATH-332

Enseignant(s) :

Mountford Thomas

Langue:

English

Summary

The course follows the text of Norris and the polycopie (which will be distributed chapter by chapter).

Content

We will follow the book of Norris beginning with a recap of basic probability.  Then we pass to the definition of Markov chains and the definition of irreducible.  We analyze notions of recurrence and transcience, particularly for irreducible chains.  We then define positive recurrence and stationary distributions before proving the convergence theorem for aperiodic positive recurrent markov chains.  The last two topics are continuous times Markov Chains and renewal theorms.

Keywords

Stationary distributions.  Irreducibility. Aperiodicity. Communicating classes.  Transcience and recurrance.  Transition matrices.  Operators.

Learning Prerequisites

Required courses

Second year probability.

Learning Outcomes

By the end of the course, the student must be able to:

Transversal skills

Teaching methods

Lectures followed by exercise sessions

Assessment methods

The greater part of the note will be determined by the final (written) exam.  There will also be small contribution by a "midterm" exam and by exercises. 

Supervision

Office hours No
Assistants No

Resources

Bibliography

Markov Chains by J. Norris is recommended but not obligatory.

Ressources en bibliothèque
Notes/Handbook

Notes will be made available

Dans les plans d'études

Semaine de référence

 LuMaMeJeVe
8-9     
9-10     
10-11     
11-12     
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
En construction
 
      Cours
      Exercice, TP
      Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand