# Degree two ergodic theorem for divergence-free stationary random fields

Abstract : We prove the ergodic theorem for surface integrals of divergence-free stationary random fields of ℝ3. Mean convergence in $\mathbb{L}^p$ spaces takes place as soon as the field is $\mathbb{L}^p$ -integrable. The condition of integrability for the pointwise convergence is expressed by a Lorentz norm. This theorem is an ergodic theorem for cocycles of degree 2, analogous to the ergodic theorem for cocycles of degree 1 proved in [1] by D. Boivin and Y. Derriennic.
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Article dans une revue
Israël Journal of Mathematics, The Hebrew University Magnes Press, 2007, 157 (1), pp.283-308. 〈10.1007/s11856-006-0012-4〉
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https://hal.archives-ouvertes.fr/hal-00336462
Contributeur : Jérôme Depauw <>
Soumis le : mardi 4 novembre 2008 - 10:54:53
Dernière modification le : jeudi 7 février 2019 - 15:00:58

### Citation

Jérôme Depauw. Degree two ergodic theorem for divergence-free stationary random fields. Israël Journal of Mathematics, The Hebrew University Magnes Press, 2007, 157 (1), pp.283-308. 〈10.1007/s11856-006-0012-4〉. 〈hal-00336462〉

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