Introduction to diffusion processes

L. Zambotti

Last updated on May 31, 2021

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.

References

  • 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.