Ergodicity of the Infinite Dimensional Fractional Brownian Motion |
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| Authors: | María J Garrido-Atienza Björn Schmalfuß |
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| Institution: | 1. Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080, Sevilla, Spain
2. Institut für Mathematik, Fakult?t EIM, Warburger Strasse 100, 33098, Paderborn, Germany
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| Abstract: | In this short note we prove that an infinite dimensional fractional Brownian motion B H of any Hurst parameter ${H \in (0, 1)}In this short note we prove that an infinite dimensional fractional Brownian motion B
H
of any Hurst parameter H ? (0, 1){H \in (0, 1)} forms an ergodic metric dynamical system. For the proof we mainly use the fundamental theorems of Kolmogorov. |
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