Sumários
Subordinators
24 Outubro 2017, 10:00 • João Guerra
Exercise: the Cauchy distribution as the ratio of normals
Subordinators and time changes. Examples: 2-alpha process, Varianve-Gamma, CGMY, Inverse normal Gaussian process.
Lévy processes and martingales.
Exercises and problems, Subordinators
19 Outubro 2017, 10:00 • João Guerra
Exercises and problems.
Subordinators.
Stable distributions and stable processes
17 Outubro 2017, 10:00 • João Guerra
The general central limit theorem.
Stable distributions.
The heavy tails for stable distributions with alpha<2.
Stable processes.
Examples of Lévy processes.
Lévy measures
12 Outubro 2017, 10:00 • João Guerra
Lévy measures: definition and basic properties.
Examples and exercises.
Poisson random measure associated to a Lévy process and the Lévy measure defined as the expected value of the Poisson random measure for a time unit.
The Lévy-Khintchine formula: proof.
Lévy processes and infinitely divisible distributions.
10 Outubro 2017, 10:00 • João Guerra
The jump-diffusion process. Basic properties.
The characteristic function of a random variable. Definition and basic properties.
Infinitely divisible distributions: definition, examples and exercises.
The Lévy processes are associated to infinitely divisible distributions: proof.