# From random partitions to fractional Brownian sheets

Abstract : We propose $\pm1$-valued random-field models that are based on random partitions of $\mathbb{N}^2$. The covariance structure of each random field is determined by the underlying random partition. Functional central limit theorems are established for the proposed models, and fractional Brownian sheets, with full range of Hurst indices, arise in the limit. Our models could be viewed as discrete analogues of fractional Brownian sheets, in the same spirit that the simple random walk is the discrete analogue of the Brownian motion.
Type de document :
Pré-publication, Document de travail
2017
Domaine :

https://hal.archives-ouvertes.fr/hal-01586410
Contributeur : Olivier Durieu <>
Soumis le : mardi 12 septembre 2017 - 17:21:10
Dernière modification le : mercredi 13 septembre 2017 - 01:11:35

### Fichier

Durieu-Wang-20170904.pdf
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### Identifiants

• HAL Id : hal-01586410, version 1
• ARXIV : 1709.00934

### Citation

Olivier Durieu, Yizao Wang. From random partitions to fractional Brownian sheets. 2017. <hal-01586410>

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## 35

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