Introduction to diffusion processes
This course takes place from October to January, 2 hours of lectures, 2 hours of tutorials per week.
This course aims to provide the basic probabilistic tools necessary for financial theory in a random universe.
- Reminder of probability.
- Gaussian processes. Brownian motion.
- Conditional expectation. Martingales.
- Stochastic integral with respect to Brownian motion.
- Stochastic calculus. Itô’s formula. Girsanov’s theorem.
- Stochastic differential equation. Markovian character of solutions. Links with some P.D.E.
- R. Durrett: Stochastic calculus. CRC Press.
- I. Karatzas, S. Shreve: Brownian motion and stochastic calculus. Springer.
- B. Oksendal: Stochastic differential equations. Springer.
- Ph. Protter: Stochastic Integration and Differential Equation. Springer.
- D. Revuz, M. Yor: Continuous martingales and Brownian motion. Springer.