Main topics are: Brownian motion (Wiener process), martingales, stochastic (Ito) integration, stochastic differential equations, diffusion processes. These tools are heavily used in financial mathematics, biology, physics, and engineering. Thus if someone wants to enter e.g. the flourishing field of financial mathematics, it is a must to complete such a course.
A good understanding of continuous time stochastic processes, including Wiener process and other diffusion processes (Ito diffusions). Understanding and competence in stochastic 116 integration and stochastic differential equations (SDE’s), strong and weak solutions, and conditions for existence and uniqueness. Practice in solving linear SDE’s, understanding the Ornstein-Uhlenbeck process. Understanding the relationship between weak solutions and the Stroock-Varadhan martingale problem; the notion of generator of a diffusion, and the related backward and forward partial differential equations.
- regular homework, and presentation or final