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

preprint2014arXivOpen access

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]H\in (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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