一类具有算子系数的二阶微分方程的平稳解

IF 0.4 Q4 STATISTICS & PROBABILITY

Theory of Probability and Mathematical Statistics Pub Date : 2022-05-16 DOI:10.1090/tpms/1171

M. Horodnii

{"title":"一类具有算子系数的二阶微分方程的平稳解","authors":"M. Horodnii","doi":"10.1090/tpms/1171","DOIUrl":null,"url":null,"abstract":"Necessary and sufficient conditions are given for the existence of a unique stationary solution to the second-order linear differential equation with bounded operator coefficients, perturbed by a stationary process. In the case when the corresponding “algebraic” operator equation has separated roots, the new representation of the stationary solution of the considered differential equation is obtained.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stationary solutions of a second-order differential equation with operator coefficients\",\"authors\":\"M. Horodnii\",\"doi\":\"10.1090/tpms/1171\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Necessary and sufficient conditions are given for the existence of a unique stationary solution to the second-order linear differential equation with bounded operator coefficients, perturbed by a stationary process. In the case when the corresponding “algebraic” operator equation has separated roots, the new representation of the stationary solution of the considered differential equation is obtained.\",\"PeriodicalId\":42776,\"journal\":{\"name\":\"Theory of Probability and Mathematical Statistics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-05-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory of Probability and Mathematical Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/tpms/1171\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and Mathematical Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tpms/1171","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

摘要

给出了算子系数有界的二阶线性微分方程在平稳过程扰动下存在唯一平稳解的充要条件。在相应的“代数”算子方程具有分离根的情况下，得到了所考虑的微分方程平稳解的新表示。

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

Stationary solutions of a second-order differential equation with operator coefficients

Necessary and sufficient conditions are given for the existence of a unique stationary solution to the second-order linear differential equation with bounded operator coefficients, perturbed by a stationary process. In the case when the corresponding “algebraic” operator equation has separated roots, the new representation of the stationary solution of the considered differential equation is obtained.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Theory of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.30

自引率

0.00%

发文量