A first-order limit law for functionals of two independent fractional Brownian motions in the critical case

Junna Bi () and Fangjun Xu ()
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Junna Bi: East China Normal University
Fangjun Xu: East China Normal University

Journal of Theoretical Probability, 2016, vol. 29, issue 3, 941-957

Abstract: Abstract We prove a first-order limit law for functionals of two independent $$d$$ d -dimensional fractional Brownian motions with the same Hurst index $$H=2/d\,(d\ge 4)$$ H = 2 / d ( d ≥ 4 ) , using the method of moments and extending a result by LeGall in the case of Brownian motion.

Keywords: Limit theorem; Fractional Brownian motion; Method of moments; Short range dependence; Primary 60F17; Secondary 60G15; 60G22 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-015-0604-1

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