Stochastic Calculus

Crédit : 6 ECTS
Langue du cours : anglais

Volume horaire

• CM : 48 h
• Volume horaire global (hors stage) : 48 h

Compétences 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

Description 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).

Mode de contrôle des connaissances

Final written exam, in class.

Pré-requis recommandés

Probability theory foundations

Bibliographie, lectures recommandées

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Enseignant responsable

CLEMENT COSCO

Enseignant responsable

MARC HOFFMANN