复平面上随机演化方程的解析解

IF 0.6 Q4 STATISTICS & PROBABILITY

Austrian Journal of Statistics Pub Date : 2023-08-15 DOI:10.17713/ajs.v52isi.1757

I. Samoilenko, G. Verovkina, T. Samoilenko

{"title":"复平面上随机演化方程的解析解","authors":"I. Samoilenko, G. Verovkina, T. Samoilenko","doi":"10.17713/ajs.v52isi.1757","DOIUrl":null,"url":null,"abstract":"We discuss a generalization of Goldstein-Kac model on a complex plane and apply probabilistic approach to construct solutions of the corresponding Cauchy problem for complex-analytic initial conditions. The method is based on reconstruction of complex-analytic functions by combination of power functions, for which corresponding solutions are the moments of evolution process.As soon as in the hydrodynamic limit the equation for our model approximates a Schrödinger-type equation, the solutions constructed for pre-limit Cauchy problem may approximate solutions for corresponding Cauchy problem for a Schrödinger-type equation.","PeriodicalId":51761,"journal":{"name":"Austrian Journal of Statistics","volume":"49 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytic Solutions of Equation for Random Evolution on a Complex Plane\",\"authors\":\"I. Samoilenko, G. Verovkina, T. Samoilenko\",\"doi\":\"10.17713/ajs.v52isi.1757\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We discuss a generalization of Goldstein-Kac model on a complex plane and apply probabilistic approach to construct solutions of the corresponding Cauchy problem for complex-analytic initial conditions. The method is based on reconstruction of complex-analytic functions by combination of power functions, for which corresponding solutions are the moments of evolution process.As soon as in the hydrodynamic limit the equation for our model approximates a Schrödinger-type equation, the solutions constructed for pre-limit Cauchy problem may approximate solutions for corresponding Cauchy problem for a Schrödinger-type equation.\",\"PeriodicalId\":51761,\"journal\":{\"name\":\"Austrian Journal of Statistics\",\"volume\":\"49 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-08-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Austrian Journal of Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17713/ajs.v52isi.1757\",\"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":"Austrian Journal of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17713/ajs.v52isi.1757","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

讨论了Goldstein-Kac模型在复平面上的推广，并应用概率方法构造了相应的复解析初始条件下的Cauchy问题的解。该方法基于幂函数组合对复解析函数进行重构，其对应解为演化过程矩。只要在水动力极限下，我们模型的方程近似于Schrödinger-type方程，极限前柯西问题的解就可以近似于相应的Schrödinger-type方程的柯西问题的解。

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

Analytic Solutions of Equation for Random Evolution on a Complex Plane

We discuss a generalization of Goldstein-Kac model on a complex plane and apply probabilistic approach to construct solutions of the corresponding Cauchy problem for complex-analytic initial conditions. The method is based on reconstruction of complex-analytic functions by combination of power functions, for which corresponding solutions are the moments of evolution process.As soon as in the hydrodynamic limit the equation for our model approximates a Schrödinger-type equation, the solutions constructed for pre-limit Cauchy problem may approximate solutions for corresponding Cauchy problem for a Schrödinger-type equation.

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

Austrian Journal of Statistics STATISTICS & PROBABILITY-

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 weeks

期刊介绍： The Austrian Journal of Statistics is an open-access journal (without any fees) with a long history and is published approximately quarterly by the Austrian Statistical Society. Its general objective is to promote and extend the use of statistical methods in all kind of theoretical and applied disciplines. The Austrian Journal of Statistics is indexed in many data bases, such as Scopus (by Elsevier), Web of Science - ESCI by Clarivate Analytics (formely Thompson & Reuters), DOAJ, Scimago, and many more. The current estimated impact factor (via Publish or Perish) is 0.775, see HERE, or even more indices HERE. Austrian Journal of Statistics ISNN number is 1026597X Original papers and review articles in English will be published in the Austrian Journal of Statistics if judged consistently with these general aims. All papers will be refereed. Special topics sections will appear from time to time. Each section will have as a theme a specialized area of statistical application, theory, or methodology. Technical notes or problems for considerations under Shorter Communications are also invited. A special section is reserved for book reviews.