Sumários
Exercises
19 Março 2018, 10:00 • João Guerra
Exercises on martingales and properties of stochastic integral.
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.
Discussion of some exercises and problems
8 Março 2018, 10:00 • João Guerra
Exercises and problems about martingales and Brownian motion.
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.
Brownian motion
1 Março 2018, 10:00 • João Guerra
Exercise involving a compound Poisson process.
Brownian motion. Definition and Basic properties.