Operator Fractional Brownian Sheet and Martingale Differences

2015/04/09 by Dai, Hongshuai, Shen, Guangjun, Xia, Wenliang
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1504.02203

Abstract

In this paper, inspired by the fractional Brownian sheet of Riemann-Liouville type, we introduce the operator fractional Brownian sheet of Riemman-Liouville type, and study some properties of it. We also present an approximation in law to it based on the martingale differences.

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• Operator Fractional Brownian Motion and Martingale Differences
• Hermite variations of the fractional Brownian sheet
• An invariance principle for fractional Brownian sheets
• Weak convergence to the fractional Brownian sheet from a Lévy sheet
• Convergence to Weighted Fractional Brownian Sheets