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Description

As a generalisation of Lamperti’s transformation, it has been proved by Alili, Chaumont, Grackzyk and Zak that a stable process in dimension d can be seen as the exponential of a Markov additive process (MAP) time changed. In this talk, we aim at describing the so called upward, respectively downward, ladder height processes associated to this MAP. We will provide a precise description in the case where d=1, and, in general, how the characteristics of this process could be derived from known identities for stable processes. This is based on a ongoing collaboration with Kyprianou, Satitkanitkul and Sengul.