有界域上有色噪声驱动的随机分数阶拉普拉斯方程及其协方差泛函

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Stochastic Models Pub Date : 2022-03-16 DOI:10.1080/15326349.2022.2045205

Nicolás Piña, T. Caraballo, E. Porcu

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引用次数: 0

摘要

摘要本文给出了平稳高斯随机场上分数拉普拉斯算子及其谱表示被定义的条件。此外，我们还研究了开有界集上加性有色噪声驱动的随机分数椭圆方程弱解的存在性和唯一性。谱方法和变分方法都用于提供解决方案。此外，导出了与该解相关联的函数协方差。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A stochastic fractional Laplace equation driven by colored noise on bounded domain, and its covariance functional

Abstract The paper provides conditions for the fractional Laplacian and its spectral representation on stationary Gaussian random fields to be well-defined. In addition, we study existence and uniqueness of the weak solution for a stochastic fractional elliptic equation driven by an additive colored noise over an open bounded set. Both spectral and variational approaches are used to provide a solution. Further, the functional covariance associated with the solution is derived.

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来源期刊

Stochastic Models 数学-统计学与概率论

CiteScore

1.30

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastic Models publishes papers discussing the theory and applications of probability as they arise in the modeling of phenomena in the natural sciences, social sciences and technology. It presents novel contributions to mathematical theory, using structural, analytical, algorithmic or experimental approaches. In an interdisciplinary context, it discusses practical applications of stochastic models to diverse areas such as biology, computer science, telecommunications modeling, inventories and dams, reliability, storage, queueing theory, mathematical finance and operations research.