Numerical simulation: probabilistic approach and Monte Carlo method

Knowledge expected at the end of the course


Master probabilistic simulation techniques (C1,N1).


Master the practice of generating random variables to simulate random models (C1,N1).


Master Monte Carlo techniques: convergence, confidence intervals, acceleration techniques, etc. (C1,N1). (C1,N1).


Learning outcomes in terms of abilities, skills and attitudes expected at the end of the course


Master the essential concepts of numerical simulation using probabilistic techniques (C1,N1)...


Know how to build tools for simulating simple random models and numerically calculate the probabilistic elements needed to exploit these models (C1,N1).


Master Monte Carlo techniques and their implications for numerical simulation(C1,N1).

The prerequisites for this course are light, and call directly on the first-year probability course PS101.

- Simulation of random variables and vectors using inversion and rejection methods. - Illustrations of the law of large numbers and the central limit theorem. - Monte-Carlo method, objectives, advantages. - Variance reduction methods.

N. Bartoli and P. Del Moral, Simulation et algorithmes stochastiques. Cépaduès Edition, 2001.E. Gobet, Monte-Carlo methods and stochastic processes. CRC Press, Boca Raton, FL, 2016.S. Ross, Simulation, Academic Press, 2002.P. Vallois, Modélisations stochastiques et simulations. Paris : Ellipses, 2007.