Stochastic calculus (M2 - 2021)
This course is a practical introduction to the theory of stochastic calculus, with an emphasis on examples and applications rather than abstract subtleties. It consists of four parts:
- Stochastic integration
- Stochastic differentiation
- Stochastic differential equations
- The lectures take place on Mondays, 13h45-15h15 and Thursdays, 8h30-11h45.
- The exercise sessions (supervised by ) take place on Mondays, 15h30-18h45.
- The final exam took place on November 8th, 14h-17h. Here is a detailed solution.
- 20.09 - stochastic processes, Brownian motion, martingales
- 23.09 - quadratic variation, local martingales
- 27.09 - isometric extension, Wiener's integral
- 30.09 - progressive processes, Ito's integral
- 04.10 - generalized Ito integral
- 07.10 - Itô processes, Itô's formula, examples
- 11.10 - exponential martingales, Novikov's criterion
- 14.10 - Girsanov's theorem, introduction to stochastic differential equations
- 18.10 - examples of stochastic differential equations, with explicit resolution
- 21.10 - Markov property, semi-group, generator, Kolmogorov equations, Fokker-Planck equation, Feynman-Kac's formula
- Calcul stochastique et modèles de diffusions (F. Comets, T. Meyre)
- Calcul stochastique et problèmes de martingales (J. Jacod)
- Brownian motion and stochastic processes (I. Karatzas, S.E. Shreve)
- An introduction to stochastic differential equations (L.C. Evans)
- Stochastic calculus (R. Durrett)