Sumários

19 Março 2018, 10:00 • João Guerra

Exercises on martingales and properties of stochastic integral.

12 Março 2018, 10:00 • João Guerra

Stochastic integral: motivation and discussion about the Riemann-Stieltjes integral.

Simple processes. Example.

Stochastic integral for simples processes. Properties and example.

Stochastic or Itô integral for adapted processes of the L^2_{a} space. Properties and example.

The identity (dB_{t})^2=dt.

8 Março 2018, 10:00 • João Guerra

Exercises and problems about martingales and Brownian motion.

5 Março 2018, 10:00 • João Guerra

Brownian motion: properties.

Exercise: the self-similar property of the Brownian motion.

Fractal properties of the Brownian motion.

Processes related to the Brownian motion: Brownian motion with drift, geometric Brownian motion and Brownian bridge.

Martingales based on the the Brownian motion. Examples.

The total variation and the quadratic variation of the Brownian motion.

1 Março 2018, 10:00 • João Guerra

Exercise involving a compound Poisson process.

Brownian motion. Definition and Basic properties.