Stochastic Calculus
Ects : 6
Enseignant responsable :
Volume horaire : 45Description du contenu de l'enseignement :
The course consists of four parts, each occupying roughly 6 hours:
- Preliminaries (Gaussian processes, Brownian motion, martingales, local martingales, variation, quadratic variation)
- Stochastic integration (Isometry extension, Wiener integral, Ito integral, martingale property)
- Stochastic differentiation (Itô processes, Itô's Formula, Girsanov's Theorem)
- Stochastic differential equations (existence and uniqueness, Markov property, generator, connections with PDEs).
Pré-requis recommandés :
Probability theory foundations
Compétence à acquérir :
This course is a practical introduction to the theory of stochastic calculus, with an emphasis on examples and applications rather than abstract subtleties. Click here for more information
Mode de contrôle des connaissances :
Final written exam, in class.
Bibliographie, lectures recommandées