Sumários

Existence and uniqueness theorem for stochastic differential equations

1 Abril 2022, 10:00 • João Guerra

Existence and uniqueness theorem for stochastic differential equations. Examples of application.

Example of explosion of solution. 
Sketch of the proof of the theorem. 

Exercises and stochastic differential equations

31 Março 2022, 13:30 • João Guerra

Exercises on the application of Itô's formula. 

Stochastic differential equations important examples: the geometric Brownian motion SDE and the Langevin equation. 

Exercises and introduction to stochastic differential equations

25 Março 2022, 10:00 • João Guerra

Exercises on the application of the Itô formula, Ito representation theorem and martingale representation theorem. 

Introduction to stochastic differential equations: motivation and one example (geometric Brownian motion SDE). 

Ito integral representation theorem and martingale representation theorem

24 Março 2022, 13:30 • João Guerra

Ito integral representation theorem. Examples.


Martingale representation theorem. Example. 

Discussion of exercises on applications of Itô formula. 

Itô formula

18 Março 2022, 10:00 • João Guerra

One-dimensional and multidimensional Itô formulas. 

Examples and exercises. 
Sketch of the proof of the one-dimensional Itô formula.