Key elements of the theory of stochastic differential equations are discussed. In addition, an introduction to algorithmic aspects is given. The following topics are covered:
- Brownian motion,
- martingales theory,
- stochastic integration (with respect to Brownian motion),
- strong and weak solutions of SDEs,
- stochastic representation of the solution of partial differential equations,
- classical approximations,
- stochastic multi-level algorithms.