The quantum decomposition associated with the Lévy white noise processes without moments

• Autorzy: Accardi L. , Riahi A. , Rebei H.
• Języki publikacji: EN

Abstrakty

EN

The theory of one-mode type Interacting Fock Space (IFS) allows us to construct the quantum decomposition associated with stochastic processes on R with moments of any order. The problem to extend this result to processes without moments of any order is still open but the Araki-Woods-Parthasarathy-Schmidt characterization of Lévy processes in terms of boson Fock spaces, canonically associated with the Lévy-Khintchine functions of these processes, provides a quantum decomposition for tchem which is based on boson creations, annihilation and preservation operators rather than on their IFS counterparts. In order to compare the two quantum decompositions in their common domain of application (i.e., the Lévy processes with moments of all orders) the first step is to give a precise formulation of the quantum decomposition for these processes and the analytical conditions of its validity. We show that these conditions distinguish three different notions of quantum decomposition of a Lévy process on R according to the existence of second or only first moments, or no moments at all. For the last class a multiplicative renormalization procedure is needed.

Słowa kluczowe

EN

quantum decomposition; Kolmogorov representation; Lévy white noise processes; Araki-Woods-Parthasarathy-Schmidt characterization

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2014
• Tom: Vol. 34, Fasc. 2
• Strony: 337--362
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Accardi L.

• Centro Vito Volterra, Facultà di Economia, Università di Tor Vergata, Via di Tor Vergata, 00133 Roma, Italy

autor

Riahi A.

• Department of Mathematics, Graduate School of Science and Technology of Hammam Sousse University of Sousse, Tunisia

autor

Rebei H.

• Department of Mathematics, Higher Institute of Applied Science and Technology of Gabes University of Gabes, Tunisia

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).