Sumários

25 Fevereiro 2025, 11:30 • João Guerra

Itô Representation Theorem and Martingale Representation Theorem. Examples.

Integration by parts formula.

Discussion of exercises on the application of Itô formula.

20 Fevereiro 2025, 11:00 • João Guerra

Multidimensional Brownian motion and multidimensional Ito processes. Definition and examples.

The multidimensional Ito formula. Examples.

Discussion of exercises about stochastic integrals and about the Ito formula.

18 Fevereiro 2025, 11:30 • João Guerra

Extensions of the stochastic integral. Spaces of processes L_{a,T} and L ^1_{a,T}

Motivation for the one-dimensional Ito formula as a stochastic chain rule derived from a second order Taylor expansion.

Ito processes. Definition and examples.

Itô formula for one-dimensional Ito processes. Examples.

13 Fevereiro 2025, 11:00 • João Guerra

Ito Stochastic integrals for adapted processes in L^2_{a,T}. Definition and basic processes.

Example.

Indefinite stochastic integral as process. Properties. Examples.

Discussion of exercises on Brownian motion and stochastic integrals.

11 Fevereiro 2025, 11:30 • João Guerra

Motivation for the definition of stochastic integral.

The Riemann-Stieltjes integral.

The L^2_{a,T} space of processes.

Simple processes. Examples. Stochastic integral for simple processes. Basic properties. Example.

Disussion of exercises about the Brownian motion.