ENSAE Paris - École d'ingénieurs pour l'économie, la data science, la finance et l'actuariat

Stochastic Calculus (ENSTA)


The course presents the basic material for stochastic calculus. It will include the following chapters.


1. Motivations: stochastic modeling, probabilistic representations of linear PDEs, stochastic control, filtering, mathematical finance.
2. Stochastic processes in continuous time: Gaussian processes, Brownian motion, (local) martingales, semimartingales, Itˆo processes.
3. Stochastic integrals: forward and Ito integrals.
4. Ito and chain rule formulae, a first approach to stochastic differential equations.
5. Girsanov formulae. Novikov and Benˆes coondition. Predictable representation of Brownian martingales.
6. Stochastic differential equations with Lipschitz coefficients. Markov flows.