Stochastic calculus (M2 - 2022)
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, 13:45-15:15 and Thursdays, 8:30-11:45.
- The exercise sessions take place on Mondays, 15:30-18:45.
- The final exam will take place on November 3, 8:45-11:45.
- 19.09 - stochastic processes, Brownian motion, martingales
- 22.09 - quadratic variation, local martingales
- 26.09 - isometric extension, Wiener's integral
- 29.09 - progressive processes, Ito's integral, generalized Ito integral
- 03.10 - Itô processes, quadratic variation and quadratic covariation
- 06.10 - integration-by-parts formula, Itô's formula, examples
- 10.10 - exponential martingales, Novikov's criterion
- 13.10 - Girsanov's theorem, introduction to stochastic differential equations
- 17.10 - examples of stochastic differential equations, with explicit resolution
- 20.10 - 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)