Itô Stochastic integral

29 Setembro 2020, 11:30 • João Guerra

Motivation for the definition of stochastic integrals.

Definition and examples of Simple processes.

Itô stochastic integral of a simple process. Definition and example. 

Definition of Itô stochastic integral for adapted processes of the class L^{2}.

The Itô isometry and basic properties of stochastic integrals. 

Example of calculation of a Itô stochastic integral by definition. 

 

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Brownian motion and martingales in continuous time

25 Setembro 2020, 12:00 • João Guerra

Filtrations in continuous time and adapted processes. Examples. 

Martingales in continuous time. Examples and exercises. 

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Brownian motion and martingales

22 Setembro 2020, 11:30 • João Guerra

Non differentiability of Brownian motion trajectories. 

The time inversion of Brownian motion. Exercise. 

The conditional expectation basic properties. 

The concept of filtration and filtered probability space. 

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

 

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Brownian motion

18 Setembro 2020, 12:00 • João Guerra

Random walk and Brownian motion. 

Definition of Brownian motion. Basic properties of Brownian motion. 

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Presentation. Stochastic processes.

15 Setembro 2020, 11:30 • João Guerra

Presentation: programme, bibliography and assessment. 

Brief description of the programme and of some basic ideas about stochastic calculus. 

Stochastic processes. Definition and examples. 

Brownian motion: definition. 

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