Monte Carlo estimates of extremes of stationary/nonstationary Gaussian processes

IF 0.8 Q3 STATISTICS & PROBABILITY Monte Carlo Methods and Applications Pub Date : 2023-05-25 DOI:10.1515/mcma-2023-2006
M. Grigoriu
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引用次数: 0

Abstract

Abstract Finite-dimensional (FD) models X d ⁢ ( t ) X_{d}(t) , i.e., deterministic functions of time and finite sets of 𝑑 random variables, are constructed for stationary and nonstationary Gaussian processes X ⁢ ( t ) X(t) with continuous samples defined on a bounded time interval [ 0 , τ ] [0,\tau] . The basis functions of these FD models are finite sets of eigenfunctions of the correlation functions of X ⁢ ( t ) X(t) and of trigonometric functions. Numerical illustrations are presented for a stationary Gaussian process X ⁢ ( t ) X(t) with exponential correlation function and a nonstationary version of this process obtained by time distortion. It was found that the FD models are consistent with the theoretical results in the sense that their samples approach the target samples as the stochastic dimension is increased.
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平稳/非平稳高斯过程极值的蒙特卡罗估计
摘要针对平稳和非平稳高斯过程X≠(t) X(t),在有界时间区间[0,τ] [0,\tau]上定义连续样本,构造了有限维(FD)模型X d¹(t) X_{d}(t),即时间的确定性函数和𝑑随机变量的有限集。这些FD模型的基函数是X¹(t) X(t)的相关函数和三角函数的特征函数的有限集合。给出了具有指数相关函数的平稳高斯过程X¹(t) X(t)的数值实例,并给出了该过程通过时间畸变得到的非平稳版本。结果表明,随着随机维数的增加,FD模型的样本越来越接近目标样本,这与理论结果一致。
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来源期刊
Monte Carlo Methods and Applications
Monte Carlo Methods and Applications STATISTICS & PROBABILITY-
CiteScore
1.20
自引率
22.20%
发文量
31
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