Syllabus
1. Girsanov's theorem and equations with a bounded Borel drift
2. Weak solutions to equations with continuous coefficients
3. Uniqueness of solutions and the Yamada-Watanabe theory
4. Stability of solutions in quadratic mean, in probability, and almost surely
Annotation
The course focuses on two topics: a) weak solutions to stochastic differential equations (existence of solutions to equations with a bounded Borel drift, subjected to an additive noise, and to equations with continuous coefficents, uniqueness of solutions in law and pathwise), b) qualitative properties of solutions (various types of Lyapunov stability).