scholarly journals Asymptotics of Maxima of Strongly Dependent Gaussian Processes

2012 ◽  
Vol 49 (04) ◽  
pp. 1106-1118 ◽  
Author(s):  
Zhongquan Tan ◽  
Enkelejd Hashorva ◽  
Zuoxiang Peng
Keyword(s):  
Correlation Function ◽  
Long Range ◽  
Gaussian Processes ◽  
Limit Distribution ◽  
Strong Dependence ◽  
Dependence Conditions ◽  
Stationary Gaussian Processes

Let {Xn(t),t∈[0,∞)},n∈ℕ, be standard stationary Gaussian processes. The limit distribution oft∈[0,T(n)]|Xn(t)| is established asrn(t), the correlation function of {Xn(t),t∈[0,∞)},n∈ℕ, which satisfies the local and long-range strong dependence conditions, extending the results obtained in Seleznjev (1991).

scholarly journals Asymptotics of Maxima of Strongly Dependent Gaussian Processes

2012 ◽  
Vol 49 (4) ◽  
pp. 1106-1118 ◽  
Author(s):  
Zhongquan Tan ◽  
Enkelejd Hashorva ◽  
Zuoxiang Peng
Keyword(s):  
Correlation Function ◽  
Long Range ◽  
Gaussian Processes ◽  
Limit Distribution ◽  
Strong Dependence ◽  
Dependence Conditions ◽  
Stationary Gaussian Processes

Let {Xn(t), t∈[0,∞)}, n∈ℕ, be standard stationary Gaussian processes. The limit distribution of t∈[0,T(n)]|Xn(t)| is established as rn(t), the correlation function of {Xn(t), t∈[0,∞)}, n∈ℕ, which satisfies the local and long-range strong dependence conditions, extending the results obtained in Seleznjev (1991).

scholarly journals Estimates for the distribution of Hölder semi-norms of real stationary Gaussian processes with a stable correlation function

2020 ◽  
pp. 25-30
Author(s):  
D. Zatula
Keyword(s):  
Correlation Function ◽  
Present Article ◽  
Gaussian Processes ◽  
Random Variables ◽  
Random Processes ◽  
Hölder Spaces ◽  
Stationary Gaussian Processes ◽  
Holder Spaces

Complex random variables and processes with a vanishing pseudo-correlation are called proper. There is a class of stationary proper complex random processes that have a stable correlation function. In the present article we consider real stationary Gaussian processes with a stable correlation function. It is shown that the trajectories of stationary Gaussian proper complex random processes with zero mean belong to the Orlich space generated by the function $U(x) = e^{x^2/2}-1$. Estimates are obtained for the distribution of semi-norms of sample functions of Gaussian proper complex random processes with a stable correlation function, defined on the compact $\mathbb{T} = [0,T]$, in Hölder spaces.

Low-frequency vibrational spectroscopy: a new tool for revealing crystalline magnetic structures in iron phosphate crystals

2021 ◽  
Vol 23 (39) ◽  
pp. 22241-22245
Author(s):  
Zihui Song ◽  
Xudong Liu ◽  
Anish Ochani ◽  
Suling Shen ◽  
Qiqi Li ◽  
...  
Keyword(s):  
Lithium Ion Batteries ◽  
Long Range ◽  
Vibrational Spectroscopy ◽  
Strong Dependence ◽  
Low Frequency ◽  
Lithium Ion ◽  
Iron Phosphate ◽  
Promising Material ◽  
Vibrational Dynamics ◽  
Magnetic Structures

In this report, the strong-dependence of low-frequency (terahertz) vibrational dynamics on weak and long-range forces in crystals is leveraged to determine the bulk magnetic configuration of iron phosphate – a promising material for cathodes in lithium ion batteries.

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