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May 2019 From random partitions to fractional Brownian sheets
Olivier Durieu, Yizao Wang
Bernoulli 25(2): 1412-1450 (May 2019). DOI: 10.3150/18-BEJ1025


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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Olivier Durieu. Yizao Wang. "From random partitions to fractional Brownian sheets." Bernoulli 25 (2) 1412 - 1450, May 2019.


Received: 1 September 2017; Revised: 1 January 2018; Published: May 2019
First available in Project Euclid: 6 March 2019

zbMATH: 07049411
MathSciNet: MR3920377
Digital Object Identifier: 10.3150/18-BEJ1025

Keywords: fractional Brownian motion , Fractional Brownian sheet , invariance principle , long-range dependence , Random field , random partition , regular variation

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability


Vol.25 • No. 2 • May 2019
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