lmat2470  2020-2021  Louvain-la-Neuve

Due to the COVID-19 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 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
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

Due to the COVID-19 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, 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
MATH

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

Title of the programme
Sigle
Credits
Prerequisites
Aims
Master [120] in Mathematics

Master [120] in Actuarial Science

Master [60] in Physics

Master [120] in Physics

Master [120] in Statistic: General