Recent Results on Approximation of Solutions of Stochastic Differential Equations. Lecture 1

Содержание: $$$$ 1. Basics of stochastic processes and stochastic differential equations $$$$ 2. Weak approximations: from Jacod-Kurtz-Protter to Milshtein-Talay $$$$ 3. Strong approximations: multilevel approach $$$$ 4. An exact simulation method for one-dimensional diffusions $$$$ 5. Stochastic Taylor expansion $$$$ 6. Schemes with high-order of weak convergence: Kusuoka, Lyons and Victoir approaches