Sumários

Stochastic integrals of adapted processes and One-dimensional Itô formula

16 Setembro 2025, 11:30 • João Guerra

Stochastic integrals of adapted processes of class L^2,a,T. Definition and basic properties. 

Example of calculation of a stochastic integral of adapted process by definition. 
Equality dB^2 = dt and the one-dimensional Itô formula as a stochastic chain rule. 
Simple example of application of Itô formula. 

Stochastic integral

15 Setembro 2025, 12:00 • João Guerra

Discussion of exercises on martingales.

Motivation for the definition of stochastic integral. 
Simples processes. Definition and examples. 
Stochastic integral for simple processes: definition and examples. 

Martingales

9 Setembro 2025, 11:30 • João Guerra

Discussion of exercises on Brownian motion properties. 

Martingales in discrete time and in continuous time: definitions and basic properties. Examples.

Brownia motion

8 Setembro 2025, 12:00 • João Guerra

Brownian motion: definition and basic properties. 

Definition and basic properties of conditional Expectation, filtrations and martingales in discrete time. 

Presentation of the course. Brownian motion.

1 Setembro 2025, 12:00 • João Guerra

Presentation of the course: Programme, bibliography, assessment. 

Introduction to stochastic calculus and its history. 
Basic concepts of stochastic processes.
Example: Poisson process. 
Physical Brownian motion.
Definition of standard Brownian motion and of Brownian motion with drift.