Due to the COVID19 crisis, the information below is subject to change,
in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
5 credits
30.0 h
Q2
Teacher(s)
Hainaut Donatien;
Language
French
Main themes
Processes, martingales et Markov chain in discrete and continuous time. Stopping times. Poisson Process, Brownian motian and Itô calculus
Aims
At the end of this learning unit, the student is able to :  
1 

Content
Part I:
 Revision of probability theory
 Martingales in discrete time
 Markov Chaine in discrete time and with a finite number of states
 Poisson processes and Poisson measures
 Continuous Markov process with a finite number of states
 Brownian motien & Itô's calculus
 Continuous time martingales
 Continuous Markov processes with infinite number of state
Evaluation methods
Due to the COVID19 crisis, the information in this section is particularly likely to change.
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, AddisonWesley, 1968.
 CHOW, Y.S. and M. TEICHER, Probability Theory: Independence, Interchangeability, Martingales, SpringerVerlag, 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
MATH