Rare-event simulation and efficient discretization for the supremum of Gaussian random fields
Rare-event simulation and efficient discretization for the supremum of Gaussian random fields
复制标题
高斯随机场上界的稀有事件模拟与高效离散化
DOI：
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发表时间：
2013
影响因子：
1.2
通讯作者：
Jingcheng Liu
中科院分区：
文献类型：
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作者：
Xiaoou Li;Jingcheng Liu
本文研究了紧集T上高斯随机场f的高偏移概率的一个经典问题，并给出了尾概率的有效计算方法：f(T) > b}。对于每一个正的ε，我们给出了在恒定时间内运行的蒙特卡罗算法，并计算了任意大b的相对误差ε的概率。效率结果适用于大型Hölder连续高斯随机场。除计算外，测度变化及其分析技术在高斯随机场的渐近分析中具有多种理论和实践意义。
In this paper we consider a classic problem concerning the high excursion probabilities of a Gaussian random field f living on a compact set T. We develop efficient computational methods for the tail probabilities ℙ{sup T f(t) > b}. For each positive ε, we present Monte Carlo algorithms that run in constant time and compute the probabilities with relative error ε for arbitrarily large b. The efficiency results are applicable to a large class of Hölder continuous Gaussian random fields. Besides computations, the change of measure and its analysis techniques have several theoretical and practical indications in the asymptotic analysis of Gaussian random fields.