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).
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 :
- 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
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.
Prerequisite : The courses MAT1322 Théorie de la mesure and MAT1371 Probabilités are an essential prerequisite.
- 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
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