{"title":"分数型白波方程的二次变分","authors":"Radomyra Shevchenko","doi":"10.1090/tpms/1192","DOIUrl":null,"url":null,"abstract":"This paper studies the behaviour of quadratic variations of a stochastic wave equation driven by a noise that is white in space and fractional in time. Complementing the analysis of quadratic variations in the space component carried out in [Correlation structure, quadratic variations and parameter estimation for the solution to the wave equation with fractional noise, Electron. J. Stat. 12 (2018), no. 2, 3639–3672] and [Generalized \n\n \n k\n k\n \n\n-variations and Hurst parameter estimation for the fractional wave equation via Malliavin calculus, J. Statist. Plann. Inference 207 (2020), 155–180], it focuses on the time component of the solution process. For different values of the Hurst parameter a central and a noncentral limit theorems are proved, allowing to construct parameter estimators and compare them to the findings in the space-dependent case. Finally, rectangular quadratic variations in the white noise case are studied and a central limit theorem is demonstrated.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On quadratic variations for the fractional-white wave equation\",\"authors\":\"Radomyra Shevchenko\",\"doi\":\"10.1090/tpms/1192\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper studies the behaviour of quadratic variations of a stochastic wave equation driven by a noise that is white in space and fractional in time. Complementing the analysis of quadratic variations in the space component carried out in [Correlation structure, quadratic variations and parameter estimation for the solution to the wave equation with fractional noise, Electron. J. Stat. 12 (2018), no. 2, 3639–3672] and [Generalized \\n\\n \\n k\\n k\\n \\n\\n-variations and Hurst parameter estimation for the fractional wave equation via Malliavin calculus, J. Statist. Plann. Inference 207 (2020), 155–180], it focuses on the time component of the solution process. For different values of the Hurst parameter a central and a noncentral limit theorems are proved, allowing to construct parameter estimators and compare them to the findings in the space-dependent case. Finally, rectangular quadratic variations in the white noise case are studied and a central limit theorem is demonstrated.\",\"PeriodicalId\":42776,\"journal\":{\"name\":\"Theory of Probability and Mathematical Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-11-26\",\"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/1192\",\"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/1192","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
On quadratic variations for the fractional-white wave equation
This paper studies the behaviour of quadratic variations of a stochastic wave equation driven by a noise that is white in space and fractional in time. Complementing the analysis of quadratic variations in the space component carried out in [Correlation structure, quadratic variations and parameter estimation for the solution to the wave equation with fractional noise, Electron. J. Stat. 12 (2018), no. 2, 3639–3672] and [Generalized
k
k
-variations and Hurst parameter estimation for the fractional wave equation via Malliavin calculus, J. Statist. Plann. Inference 207 (2020), 155–180], it focuses on the time component of the solution process. For different values of the Hurst parameter a central and a noncentral limit theorems are proved, allowing to construct parameter estimators and compare them to the findings in the space-dependent case. Finally, rectangular quadratic variations in the white noise case are studied and a central limit theorem is demonstrated.