This course will be an introduction to simulation methods for a wide range of stochastic models.
The emphasis is on the construction of the numerical approximations with a limited discussion of their accuracy and computational cost, and almost no stochastic numerical analysis.
The topics covered include:
random and quasi-random number generation;
basics of Monte Carlo and Quasi-Monte Carlo simulation;
Multilevel Monte Carlo and Multilevel QMC methods;
sensitivity analysis;
stochastic dierential equations;
continuous-time Markov processes;
stochastic PDEs;
stochastic approximation;
estimation of invariant measures;
nested estimation;
stochastic gradient method.
Practicals will be performed in either Matlab or C.