{"title":"分段常系数随机热方程的精确变分及其在参数估计中的应用","authors":"M. Zili, Eya Zougar","doi":"10.1090/tpms/1099","DOIUrl":null,"url":null,"abstract":"We expand the quartic variations in time and the quadratic variations in space of the solution to a stochastic partial differential equation with piecewise constant coefficients. Both expansions allow us to deduce an estimation method of the parameters appearing in the equation.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2020-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/tpms/1099","citationCount":"7","resultStr":"{\"title\":\"Exact variations for stochastic heat equations with piecewise constant coefficients and application to parameter estimation\",\"authors\":\"M. Zili, Eya Zougar\",\"doi\":\"10.1090/tpms/1099\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We expand the quartic variations in time and the quadratic variations in space of the solution to a stochastic partial differential equation with piecewise constant coefficients. Both expansions allow us to deduce an estimation method of the parameters appearing in the equation.\",\"PeriodicalId\":42776,\"journal\":{\"name\":\"Theory of Probability and Mathematical Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2020-08-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1090/tpms/1099\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory of Probability and Mathematical Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/tpms/1099\",\"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/1099","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Exact variations for stochastic heat equations with piecewise constant coefficients and application to parameter estimation
We expand the quartic variations in time and the quadratic variations in space of the solution to a stochastic partial differential equation with piecewise constant coefficients. Both expansions allow us to deduce an estimation method of the parameters appearing in the equation.