Characterization of Lévy Processes by a duality formula and related results

  • Processes with independent increments are characterized via a duality formula, including Malliavin derivative and difference operators. This result is based on a characterization of infinitely divisible random vectors by a functional equation. A construction of the difference operator by a variational method is introduced and compared to approaches used by other authors for L´evy processes involving the chaos decomposition. Finally we extend our method to characterize infinitely divisible random measures.

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Author:Rüdiger Murr
Series (Serial Number):Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint (2011, 02)
Document Type:Preprint
Date of Publication (online):2011/05/11
Year of Completion:2011
Publishing Institution:Universität Potsdam
Release Date:2011/05/11
RVK - Regensburg Classification:SI 990
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht