rosenblatt sheet
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2019 ◽  
Vol 39 (2) ◽  
pp. 385-401
Author(s):  
Thi Thanh Diu Tran

Let Zt q,H t∈[0,1]d denote a d-parameter Hermite random field of order q ≥ 1 and self-similarity parameter H = H₁, . . . ,Hd ∈  ½, 1d. This process is H-self-similar, has stationary increments and exhibits long-range dependence. Particular examples include fractional Brownian motion q = 1, d = 1, fractional Brownian sheet q = 1, d ≥ 2, the Rosenblatt process q = 2, d = 1 as well as the Rosenblatt sheet q = 2, d ≥ 2. For any q ≥ 2, d ≥ 1 and H ∈ ½, 1d we show in this paper that a proper renormalization of the quadratic variation of Zq,H converges in L2Ω to a standard d-parameter Rosenblatt random variable with self-similarity index H' = 1 + 2H − 2/q.


2015 ◽  
Vol 10 (4) ◽  
pp. 985-1004 ◽  
Author(s):  
Guangjun Shen ◽  
Xiuwei Yin ◽  
Dongjin Zhu

2015 ◽  
Vol 13 (4) ◽  
pp. 2215-2227 ◽  
Author(s):  
Guangjun Shen ◽  
Xiuwei Yin ◽  
Litan Yan
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