Martingales et calcul stochastique

TL;DR

This lecture note provides a comprehensive overview of martingales and stochastic calculus, covering discrete and continuous-time processes, convergence theorems, Brownian motion, Itô integrals, and stochastic differential equations, suitable for master-level students.

Contribution

It offers a detailed, corrected set of lecture notes on martingales and stochastic calculus, tailored for advanced mathematics students, including exercises and practical examples.

Findings

Covers key concepts in martingales and stochastic calculus.

Includes corrected exercises for better understanding.

Provides foundational knowledge for advanced stochastic processes.

Abstract

Lecture notes for a master-level mathematics course on martingales and stochastic calculus, held at the University of Orl\'eans, France. With corrected exercises. Contents: Discrete-time martingales, stopping times, convergence theorems. Brownian motion, It\^o integrals, stochastic differential equations, diffusions. ----- Notes d'un cours de Master 2 en math\'ematiques, donn\'e \`a l'Universit\'e d'Orl\'eans. Avec exercices corrig\'es. Contenu: Martingales \`a temps discret, temps d'arr\^et, th\'eor\`emes de convergence. Mouvement Brownien, int\'egrale d'It\^o, \'equations diff\'erentielles stochastiques, diffusions.