Processus stochastiques (statistique)

lmat2470  2021-2022  Louvain-la-Neuve

Processus stochastiques (statistique)
5.00 credits
30.0 h
Q2
Teacher(s)
Language
French
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-homegenous
  • To infer the infinitesimal dynamics of a function driven by a Brownian motion, with the help of stochastic calculus.
 
Content
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
Evaluation methods
Each student receives 5 exercices to solve. He writes up the solutions and orally presents them to the professor. who may ask theoretical questions related to the subject of the proposed exercices.
Other information
Prerequisite : The courses MAT1322 Théorie de la mesure and MAT1371 Probabilités are an essential prerequisite.
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 [120] in Statistics: General

Master [120] in Mathematics

Master [120] in Physics

Master [120] in Actuarial Science

Master [60] in Physics