随机初始条件下Airy方程的研究

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2022-11-25 DOI:10.1214/23-ecp522

L. Sakhno

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引用次数: 1

摘要

本文研究了由平稳过程给出的随机初始数据的Airy方程均方解的性质。给出了解的连续模的结果，并描述了协方差函数的性质。给出了$\varphi$-亚高斯初始条件下解的上界分布。提供了几个例子来说明结果。将所得结果推广到分数阶Airy方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Investigation of Airy equations with random initial conditions

The paper investigates properties of mean-square solutions to the Airy equation with random initial data given by stationary processes. The result on the modulus of continiuty of the solution is stated and properties of the covariance function are described. Bounds for the distributions of the suprema of solutions under $\varphi$-sub-Gaussian initial conditions are presented. Several examples are provided to illustrate the results. Extension of the results to the case of fractional Airy equation is given.

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来源期刊

Electronic Communications in Probability 工程技术-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.