• Bernoulli
  • Volume 25, Number 2 (2019), 1412-1450.

From random partitions to fractional Brownian sheets

Olivier Durieu and Yizao Wang

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We propose discrete 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.

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Bernoulli, Volume 25, Number 2 (2019), 1412-1450.

Received: September 2017
Revised: January 2018
First available in Project Euclid: 6 March 2019

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fractional Brownian motion fractional Brownian sheet invariance principle long-range dependence random field random partition regular variation


Durieu, Olivier; Wang, Yizao. From random partitions to fractional Brownian sheets. Bernoulli 25 (2019), no. 2, 1412--1450. doi:10.3150/18-BEJ1025.

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