Sumários
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.
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.
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.