Define the incremental fractional Brownian field with parameter H ∈ （0, 1） by ZH（τ, s） = BH（s-＋τ） - BH（S）, where BH（s） is a fractional Brownian motion with Hurst parameter H ∈ （0, 1）. We firstly deriv...Define the incremental fractional Brownian field with parameter H ∈ （0, 1） by ZH（τ, s） = BH（s-＋τ） - BH（S）, where BH（s） is a fractional Brownian motion with Hurst parameter H ∈ （0, 1）. We firstly derive the exact tail asymptoties for the maximum MH＊（T） = max（τ,s）∈[a,b]×[0,T] ZH（τ, s）/τH of the standardised fractional Brownian motion field, with any fixed 0 〈 a 〈 b 〈 ∞ and T 〉 0; and we, furthermore, extend the obtained result to the ease that T is a positive random variable independent of {BH（s）, s ≥ 0}. As a by-product, we obtain the Gumbel limit law for MH＊r（T） as T →∞.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11326175 and 71471090)Natural Science Foundation of Zhejiang Province of China(Grant No.LQ14A010012)+2 种基金Research Start-up Foundation of Jiaxing University(Grant No.70512021)China Postdoctoral Science Foundation(Grant No.2014T70449)Natural Science Foundation of Jiangsu Province of China(Grant No.BK20131339)
文摘Define the incremental fractional Brownian field with parameter H ∈ （0, 1） by ZH（τ, s） = BH（s-＋τ） - BH（S）, where BH（s） is a fractional Brownian motion with Hurst parameter H ∈ （0, 1）. We firstly derive the exact tail asymptoties for the maximum MH＊（T） = max（τ,s）∈[a,b]×[0,T] ZH（τ, s）/τH of the standardised fractional Brownian motion field, with any fixed 0 〈 a 〈 b 〈 ∞ and T 〉 0; and we, furthermore, extend the obtained result to the ease that T is a positive random variable independent of {BH（s）, s ≥ 0}. As a by-product, we obtain the Gumbel limit law for MH＊r（T） as T →∞.
