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

2014/11/18 by María J. Garrido-Atienza, María J. Garrido–Atienza, Kening Lu +5 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Financial Risk and Volatility Modeling #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.DS

paper · pdf · doi:10.48550/arxiv.1411.4765

18 pages

arxiv created 2014/11/18 · openalex publication_date 2014/11/18 · arxiv updated 2014/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Random dynamical systems for stochastic evolution equations driven by multiplicative fractional Brownian noise with Hurst parameters H∈ (1/3,1/2]

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