Itô Formula

2 Outubro 2017, 11:30 • João Guerra

Itô processes. Definition. 

Itô Formula: the one-dimensional formula. Examples.

The multidimensional Itô formula. Examples. 

---

Stochastic integrals

29 Setembro 2017, 12:00 • João Guerra

Stochastic integrals and stochastic differential equations: motivation.

Riemann-Stieltjes integration and why it cannot be applied to stochastic integrals. 

Stochastic integrals for simple processes: definition, main properties and examples. 

Stochastic integrals for adapted processes: definition, main properties and example. 

---

Martingales

27 Setembro 2017, 08:00 • João Guerra

Martingales in Discrete time. Examples. 

Martingales in continuous time. Definition and basic properties. 

Examples and exercises on Martingales that depend on the Brownian motion. 

---

Brownian motion. Martingales in discrete time.

22 Setembro 2017, 12:00 • João Guerra

Brownian motion.  Main properties. 

Conditional Expectation. Main properties. 

Martingales in discrete time. Definition and main properties. Example. 

---

Presentation of the course

20 Setembro 2017, 08:00 • João Guerra

Programme. Bibliography. Presentation of the course.

Brief history of stochastic calculus.

Stochastic process. Definition.

Brownian motion. Definition.

Brownian motion as a limit  of random walks.

---