This course aims to provide an introduction to the numerical solution of stochastic differential equations. The presentation of the most used numerical techniques is equipped by the analysis of their most relevant properties in terms of accuracy, stability and conservation of invariance laws associated to the dynamics. The lectures also contain a substantive lab part (in Matlab), helpful to confirm the theoretical properties and provide an experimental evidence of the effectiveness of the presented approaches.

Outline of the lectures:

• discretized Wiener process;
• simulation of stochastic integrals;
• one-step methods for SDEs: Euler-Maruyama and Milstein methods, stochastic theta-methods, stochastic Runge-Kutta methods;
• strong and weak convergence;
• linear stability analysis;
• nonlinear stability analysis;
• principles of stochastic geometric numerical integration.