********************************************************************* SEMINARI DI PROBABILITA' E STATISTICA MATEMATICA DIPARTIMENTO DI MATEMATICA "G. PEANO" UNIVERSITA' DEGLI STUDI DI TORINO *********************************************************************

Nell'ambito delle "Lezioni Lagrangiane" del Dipartimento di Matematica "G. Peano", Università degli Studi di Torino, Via Carlo Alberto 10,

giovedì 14 Maggio 2015 alle ore 15:00 in Aula Magna,

Il Prof _ANDREAS KYPRIANOU_ (Department of Mathematical Sciences, University of Bath)

terrà un seminario dal titolo

_DEEP FACTORISATION OF THE STABLE PROCESS_

Abstract:

The Lamperti-Kiu transformation for real-valued self-similar Markov processes (rssMp) states that, associated to each rssMp via a space-time transformation, is a Markov additive process (MAP). In the case that the rssMp is taken to be an α-stable process with α ∈ (0,2), the characteristics of the matrix exponent of the semi-group of the embedded MAP (the Lamperti-stable MAP) are computed. Specifically, the matrix exponent of the Lamperti-stable MAP’s transition semi-group can be written in a compact form using only gamma functions. Just as with Lévy processes, there exists a factorisation of the (matrix) exponents of MAPs, with each of the two factors uniquely characterising the ascending and descending ladder processes, which themselves are again MAPs. To our knowledge, not a single example of such a factorisation currently exists in the literature. In this talk we provide a completely explicit Wiener-Hopf factorisation for the Lamperti-stable MAP. As a consequence of our methodology, we also get additional new results concerning space-time invariance properties of stable processes.

Tutti gli interessati sono invitati a partecipare.

-- Federico Polito

Department of Mathematics University of Torino Via Carlo Alberto, 10 10123, Torino, Italy Email: federico.polito@unito.it Tel: +39 011 6702937 Web: www.federicopolito.it