Positive Self-similar Markov Processes

Abstract

This course will look at the theory of positive self-similar Markov processes. We shall understand their bijection with the class of (exponentially) killed Lévy processes through the Lamperti transform as well as looking at some particular examples. We shall use the theory to analyse path properties of a particular class of Lévy processes called stable processes.

A useful text

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Some interesting research papers

• Lamperti (1972) Semi-stable Markov processes.
• Caballero and Chaumont (2006) Conditioned stable Lévy processes and the Lamperti representation.
• Kyprianou, Pardo and Watson (2013) Hitting distributions of alpha-stable processes via path censoring and self-similarity.

Notes from the starboard

• (14.10.13) Lecture 1: here
• (21.10.13) Lecture 2: here
• (28.10.13) Lecture 3: here
• (04.11.13) Lecture 4: No lecture
• (11.11.13) Lecture 5: here
• (18.11.13) Lecture 6: here
• (25.11.13) Lecture 7: here (From Mexico city)
• (02.12.13) Lecture 8: here
• (09.11.13) Lecture 9: here
• (16.11.13) Lecture 10: No lecture