{"title":"Investigation of Airy equations with random initial conditions","authors":"L. Sakhno","doi":"10.1214/23-ecp522","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2022-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Communications in Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/23-ecp522","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
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.
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.
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