# Processus stochastiques (statistique)

lmat2470  2022-2023  Louvain-la-Neuve

Processus stochastiques (statistique)
5.00 credits
30.0 h
Q2
Teacher(s)
Language
Prerequisites
The courses MAT1322 Measurement Theory and MAT1371 Probability are an absolute prerequisite
Main themes
Processes, martingales et Markov chain in discrete and continuous time. Stopping times. Poisson Process, Brownian motian and Itô calculus
Learning outcomes
 At the end of this learning unit, the student is able to : 1 To choice the most adapted process for modeling a random phenomenon.To analyze the properties of discrete and continuous processes.To construct martingale processes.To analyze the stability of a Markov chain.To use Poisson counting processes, homogenous and non-homegenousTo infer the infinitesimal dynamics of a function driven by a Brownian motion, with the help of stochastic calculus.
Content
This course is a detailled introduction to stochastic processes in discrete and continuous time:
Part I:
1. Revision of probability theory
2. Martingales in discrete time
3. Markov Chaine in discrete time and with a finite number of states
Part II:
1. Poisson processes and Poisson measures
2. Continuous Markov process with a finite number of states
3. Brownian motien & Itô's calculus
4. Continuous time martingales
5. Continuous Markov processes with infinite number of state
Teaching methods
15 lectures of 2 hours
Evaluation methods
Written exam
Other information
A first course in probability and statistics : "LMAT1271 Calcul des probabilités et analyse statistique"   or equivalent, and eventually "LMAT1371 Théorie des probabilités".
Online resources
Lecture notes are available on Moodle
Bibliography
• NEVEU, J., Martingales à temps discret, Masson, 1972. BREIMAN, L., Probability, Addison-Wesley, 1968.
• CHOW, Y.S. and M. TEICHER, Probability Theory: Independence, Interchangeability, Martingales, Springer-Verlag, 1987.
• CHUNG K.L., A Course in Probability Theory. Harcourt, Brace & World Inc., 1968.
• KARLIN S. and H.M. TAYLOR, A First Course in Stochastic Processes, Academic Press, 1975.
Teaching materials
• matériel sur moodle
Faculty or entity

#### Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Master [60] in Physics

Master [120] in Mathematics

Master [120] in Actuarial Science

Master [120] in Statistics: General

Master [120] in Physics