The courses MAT1322 Measurement Theory and MAT1371 Probability are an absolute prerequisite
Processes, martingales et Markov chain in discrete and continuous time. Stopping times. Poisson Process, Brownian motian and Itô calculus
At the end of this learning unit, the student is able to :
This course is a detailled introduction to stochastic processes in discrete and continuous time:
- 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
15 lectures of 2 hours
A first course in probability and statistics : "LMAT1271 Calcul des probabilités et analyse statistique" or equivalent, and eventually "LMAT1371 Théorie des probabilités".
Lecture notes are available on Moodle
- 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.
- matériel sur moodle
Faculty or entity