This course is a concise introduction to random processes with modelling and simulation in mind. We will describe and study some basic tools that permit to model time/space random phenomena. It deals with key ingredients involved in modelization and decision theory hand in hand with statistical and operational research techniques. Last but not least, stochastic modelling spreads in a wide range of field such as (non exhaustive list) image processing, biology, physics etc...
1.Markov chains; 2.Renewal processes; 3.Poisson process; 4.Jump Markov processes; 5.Queues.
Probability theory and Applications 1.
Some knowledge in the topics of Probability theory and Applications 2 will facilitate.
Continuous assesment (CC) ; written final test (E).
N1 = 1/3 *CC +2/3*E1
Durrett, R. “Essential of Stochastic processes”, Springer Verlag, New York, 1999.
Ferrari, P. A., Galves, A. “Coupling and regeneration for stochastic processes” téléchargeable à http://www.ime.usp.br/~pablo/book/oct2001/oct2001.pdf
Grimmett, G., Stirzaker, D. “Probability and Random Processes”, Oxford 3 edition 2001