Martingales in discrete time

1 Março 2017, 09:00 • João Guerra

Filtrations.

Martingales in discrete time. Definition, basic properties and examples.

The martingale transform or the stochastic integral in discrete time.

Martingales and fair games.

An example: the doubling bet strategy in a game.

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Stochastic processes; conditional expectation.

24 Fevereiro 2017, 09:00 • João Guerra

Different concepts of equivalence between stochastic processes. Example. 

Different concepts of continuity for stochastic processes. Example.

The Kolmogorov continuity criterion for the continuity of trajectories of a stochastic process. 

Conditional Expectation. Definition and basic properties. 

Interpretation of the conditional expectation as the orthogonal projection of a random variable in L^2 into a subspace of L^2. 

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Introduction

22 Fevereiro 2017, 09:00 • João Guerra

Presentation of the course. Syllabus, bibliography and assessment.

What is stochastic calculus? Main topics and a very brief history of stochastic calculus.

Stochastic processes: basic definitions and examples.

 

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