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Lévy-areas of Ornstein-Uhlenbeck processes in Hilbert-spaces


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Opened Access Lévy-areas of Ornstein-Uhlenbeck processes in Hilbert-spaces

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Author: Garrido Atienza, María José
Lu, Kening
Schmalfuss, Björn
Coordinator/Director: Sadovnichiy, Victor A.
Zgurovsky, Mikhail Z.
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2015
Published in: Continuous and distributed systems II: theory and applications
ISBN/ISSN: 9783319190747
Document type: Chapter of Book
Abstract: In this paper we investigate the existence and some useful properties of the Lévy areas of Ornstein-Uhlenbeck processes associated to Hilbert-space-valued fractional Brownian-motions with Hurst parameter H ∈ (1/3, 1/2]. We prove that this stochastic area has a Hölder-continuous version with sufficiently large Hölder-exponent and that can be approximated by smooth areas. In addition, we prove the stationarity of this area.
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DOI: 10.1007/978-3-319-19075-4_10

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