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"
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.