Generalization of Feynman-Kac formula for nonlinear and BVP problems

9 Junho 2010, 10:00 Juan António Acebron de Torres

The generalization of the Feynman-Kac formula for nonlinear parabolic problems based on forward-backward stochastic differential equations(FBSDEs) has been introduced. Moreover, several numerical methods for solving FBSDEs has been shown. Finally, it has been discussed how a boundary value parabolic problem can be solved by mean of the generalized Feynman-Kac formula, and analyzed several methods to compute accurately the first exit time.

Connection with linear PDEs: The Feynman-Kac formula

2 Junho 2010, 10:00 Juan António Acebron de Torres

It has been discussed the Feynman-Kac formula, and how the solution of linear elliptic and parabolic PDEs can be obtained through an expected value of a functional of a suited stochastic process, solution of an Ito stochastic differential equation.

Weak convergence schemes and numerical stability

26 Maio 2010, 10:00 Juan António Acebron de Torres

Several numerical schemes of weak order of convergence has been discussed, as well as analyzed the stability focusing mostly in stiff problems. The concept of A-stability for stochastic differential equations has been introduced based on asymptotic stability, and mean square stability. Some numerical examples were given to show in practice how it works. 

Stochastic Taylor expansion and strong numerical schemes

19 Maio 2010, 10:00 Juan António Acebron de Torres

The stochastic Taylor expansion was introduced, along with the two different ways of measuring the order of convergence, strong and weak. In addition, some numerical schemes based on the stochastic Taylor expansion was theoretically discussed analyzing their order of convergence, as well as, implementend in practice for solving numerically a few simple SDEs.

Stochastic differential equations

12 Maio 2010, 10:00 Juan António Acebron de Torres

Today it has been shown what a stochastic differential equation is, and their different types of solutions depending on the interpretation of the stochastic integral (Ito or Stratonovich). Moreover, for the case of linear problems it has been discussed several ways to solve them.