Syllabus
1. The Burkholder-Davis-Gundy inequality.
2. Linear equations.
3. Basic results on existence and uniqueness of strong solutions to equations with Lipschitz coefficients.
4. Representation of continuous martingales by time-changes and stochastic integrals.
Annotation
The lectures are devoted to fundamental theorems on existence, uniqueness and properties of strong and/or weak solutions to stochastic differential equations. Knowledge of basic results from stochastic analysis is presupposed.