Conditional Expectation and Martingales in Discrete time

25 Fevereiro 2019, 10:00 • João Guerra

Conditional expectation: definition and properties. 

Examples and exercises. 

Martingales in discrete time: definition and basic properties. 

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Stochastic Processes

21 Fevereiro 2019, 10:00 • João Guerra

Stationary stochastic processes. 

Processes with stationary and independent increments. 

Examples. 

The Poisson process. 

Equivalent processes and indistinguishable processes. Example

Continuity in probability, continuity in mean of order p and continuity of trajectories. Example. 

The Kolmogorov continuity criterion.

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Introduction to Stochastic Calculus

18 Fevereiro 2019, 10:00 • João Guerra

Presentation of the course programme, bibliography and assessment. 

Basic ideas of stochastic calculus and motivation. 

Brief historical presentation of Brownian motion and stochastic calculus. 

Review of stochastic processes: Definition, Markov processes, finite dimensional distributions.

Examples: Random Walk and White noise process. 

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