Mini-course "Theory and Applications of Stochastic Differential Equations"

On December 16-21 associate professor of Falparaiso University  (Chile) Jean-Francois Jabir read the mini-course "Theory and Applications of Stochastic Differential Equations"

Program

I           Fundamental notions of stochastic processes and stochastic calculus.

·        Some basic definitions.

·        The Brownian motion.

·        Ito integral and Ito formula.

 

II          Preliminaries on Stochastic Differential Equations

·        Generic form and basic properties.

·        Ordinary Differential Equations and Stochastic Differential Equations.

·        Ito diffusion processes and link with Markov processes.

 

III         Theory of Stochastic Differential Equations and applications

The principle of causality and the notion of strong solution to a SDE.

Construction and uniqueness and properties of a strong solution.

The notion of weak solutions and its link with strong solutions.

Examples in Physics, in Finance and some applications.

The martingale problems related to a SDE.

Link between PDE and SDEs.

Density estimates and strong uniqueness results for singular SDEs.

IV        SDEs of McKean-Vlasov type and their applications.

Historical background and link with nonlinear pdes and propagation of chaos.

Some well-posedness results.

Applications in Physics and recent applications in Economy.