Sumários
14 Março 2024, 11:00
•
João Guerra
One-dimensional Itô formula.
Examples.
Multidimensional Brownian motion.
Multidimensional Itô processes.
Multidimensional Itô formula.
Examples.
Discussion of exercises about martingales and stochastic integrals.
12 Março 2024, 11:30
•
João Guerra
Indefinite stochastic integral. Properties of the stochastic integral as a process.
Motivation for the Itô formula: heuristic derivation of the Itô by the 2nd order Taylor formula as a stochastic chain rule.
Itô process definition.
The one-dimensional Itô formula. Examples.
7 Março 2024, 11:00
•
João Guerra
Definition of stochastic integrals for adapted processes. Example of computation of a stochastic integral by definition.
Main properties of stochastic integrals.
Discussion of exercises on Brownian motion and its properties.
5 Março 2024, 11:30
•
João Guerra
Riemann-Stieltjes integrals.
Motivation for the probabilistic definition of stochastic integrals.
Stochastic integrals for simple processes. Definition and properties. Examples.
29 Fevereiro 2024, 11:00
•
João Guerra
Discussion of exercises and problems on:
1) Probability and stochastic processes
2) Martingales
3) Brownian motion