Sumários

31 Março 2023, 11:00 • João Guerra

Stochastic Differential Equations. Existence and uniqueness theorem: proof and examples.

Linear stochastic differential equations.

Examples and exercises.

29 Março 2023, 10:00 • João Guerra

Stochastic Differential Equations. Motivation, examples: geometric Brownian motion and Langevin Equation.

The existence and uniqueness theorem. Example.

22 Março 2023, 10:00 • João Guerra

Itô representartion theorem and martingale representation theorem.

Exercises.

17 Março 2023, 11:00 • João Guerra

Multidimensional Brownian motion and multidimensional Itô processes.

Multidimensional Itô formula. Examples.

Discussion of Exercises on the application of Ito formula.

15 Março 2023, 10:00 • João Guerra

Motivation: Taylor formula and Itô formula.

Itô processes.

One-dimensional Ito formula for Itô processes.

Examples and exercises.

Sketch of the proof of the one-dimensional Ito formula.