Sumários

Girsanov Theorem

26 Abril 2023, 10:00 • João Guerra

Girsanov Theorem. Discussion and examples. 

Exercises. 

Kolmogorov Backward and forward equations

21 Abril 2023, 11:00 • João Guerra

The heat equation and Brownian motion. 

General definition of the infinitesimal generator of a diffusion and its domain. 
The backward and forward Kolmogorov Equations (or Fokker-Planck Equation). Examples.
Discussion of exercises about infinitesimal generators. 

Exercises

19 Abril 2023, 10:00 • João Guerra

Exercises on Stochastic Differential Equations and relationships between SDE's and PDE's trough Feynman-Kac formulas. 

Partial differential equations and Stochastic differential Equations

14 Abril 2023, 11:00 • João Guerra

Infinitesimal generators associated to diffusions. 

PDE's and SDE's. Feynman-Kac formulas. Proofs and examples. 
Exercises on stochastic differential equations. 

Numerical Methods for stochastic differential equations

12 Abril 2023, 10:00 • João Guerra

Numerical methods for stochastic differential equations. Euler scheme and Milstein scheme. 

Examples and exercises on stochastic differential equations.