The lecture will cover the following topics (not exhaustive)

• Brownian motion 
• Numerical discretization of stochastic differential equations
• Monte Carlo methods
• Representations of random fields
• Modelling with stochastic differential equations
• Applications

1. D. Higham, D. and  Kloeden, P.  An introduction to the numerical simulation of stochastic differential equations. SIAM, 2021
2. E. Kloeden, E. Platen and H. Schurz. Numerical Solution of SDEs through computer experiments. Springer, Berlin, 2002
3. B. Lapeyre, E. Pardoux, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press, 2003.
4. B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, 2003
5. Lord, G. J., Powell, C. E., and Shardlow, T. An introduction to computational stochastic PDEs (Vol. 50). Cambridge University Press, 2014