Abstract: This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations
Objective: This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations.
Content
- Stochastic processes
- Brownian motion
- Continuous time martingales
- Ito's theory of stochastic integration
- Ito's formula
- Existence and uniqueness theorem for solutions of stochastic differential equations
- Girsanov's theorem and the Feynman-Kac formula
- The martingale representation theorem
- Créateur de cours: Boubakeur Labed