Stochastic calculus  -  13 lectures+exercice sessions

Chap 1: Stochastic processes
Chap 2: Brownian Motion
Chap 3: Continuous time martingales
Chap 4: Stochastic Integral
Chap 5: Stochastic Differential Equations.


(few) References :

-   Jean-Francois Le Gall, Mouvement brownien, martingales et calcul stochastique, Mathématiques et Applications, https://doi-org.ezproxy.universite-paris-saclay.fr/10.1007/978-3-642-31898-6
(also handout of Prof. Le Gall lecture easy to find on google)

-  Damien Lamberton and Bernard Lapeyre, Introduction to Stochastic Calculus Applied to Finance , Edition 2nd Edition, First Published 2007, Pub. Location New York, Imprint Chapman and Hall/CRC
DOI https://doi.org/10.1201/9781420009941

-  Ioannis Karatzas and Steven E. Shreve, Brownian Motion and Stochastic Calculus, Series Title Graduate Texts in Mathematics, https://doi.org/10.1007/978-1-4612-0949-2

-  F. Comets and Thierry Meyre – Calcul stochastique et modèles de diffusions : Cours et exercices corrigés, Dunod, 2006, Coll. Sciences, sup. iii


Tentative schedule :

1. Lectures  Stoch Process   
2. Exercice  Stoch Process   
3. Lecture   Brownian Motion
4. Exercice  B.M.  
5. Lecture   Continuous time martingale (and exercice BM)  
6. Exercice  Continuous time martingale  
7. Lecture   Stochastic Integral  
8. Lecture   Stochastic Integral / Exercice Stochastic Integral
9  Exercice  Stochastic Integral exercice
10 Exercice  Stochastic Integral / Lecture S.D.E.
11 Lecture   S.D.E.
12 Exercice  S.D.E.