Lecture to be replaced by a new lecture in December

24 Outubro 2016, 11:30 • João Guerra

Lecture to be replaced by a new lecture in December (professor in a conference in England). 

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Subordinators

21 Outubro 2016, 11:00 • João Guerra

Subordinators: definition, characterization, examples and exerciases. 

alfa-stable subordinators, (1/2)-stable subordinator, gamma subordinators, inverse gaussian subordinators. 

 

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Stable processes

17 Outubro 2016, 11:30 • João Guerra

Exercises. 

Examples of Lévy processes. 

The jump-diffusion process as an interlaced process. 

Stable processes. Examples. 

Self-similar processes. 

The rotational invariant stable processes as self-similar processes. 

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Stable distributions

14 Outubro 2016, 11:00 • João Guerra

Stable distributions: definitions, basic properties and examples. 

Heavy tails for stable distributions with alpha<2.

Lévy processes: definition, connection with infinitely divisible distributions and proof of the Lévy-Khintchine general characteristic function for Lèvy processes. 

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Infinitely divisible distributions. Lévy-Khintchine formula.

10 Outubro 2016, 11:30 • João Guerra

Infinitely divisible distributions. Examples and exercises. 

Lévy measures. Examples and exercises. 

Lévy-Khintchine formula. Proof.

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