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arXiv · 1411.4765

L\'evy-areas of Ornstein-Uhlenbeck processes in Hilbert-spaces

María J. Garrido-Atienza·Kening Lu·Björn Schmalfuss
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Abstract

In this paper we investigate the existence and some useful properties of the L\'evy areas of Ornstein-Uhlenbeck processes associated to Hilbert-space-valued fractional Brownian-motions with Hurst parameter $H\in (1/3,1/2]$. We prove that this stochastic area has a H\"older-continuous version with sufficiently large H\"older-exponent and that can be approximated by smooth areas. In addition, we prove the stationarity of this area.

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María J. Garrido-Atienza, Kening Lu, Björn Schmalfuss. 2014-11-18. L\'evy-areas of Ornstein-Uhlenbeck processes in Hilbert-spaces. https://arxiv.org/abs/1411.4765

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