{"title":"变化环境中的加尔顿-沃森θ过程","authors":"S. Sagitov, Yerakhmet Zhumayev","doi":"10.1515/eqc-2024-0001","DOIUrl":null,"url":null,"abstract":"\n <jats:p>We consider a special class of Galton–Watson theta-processes in a varying environment fully defined by four parameters, with two of them <jats:inline-formula id=\"j_eqc-2024-0001_ineq_9999\">\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:mi>θ</m:mi>\n <m:mo>,</m:mo>\n <m:mi>r</m:mi>\n <m:mo stretchy=\"false\">)</m:mo>\n </m:mrow>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_eqc-2024-0001_eq_0224.png\" />\n <jats:tex-math>{(\\theta,r)}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula> being fixed over time <jats:italic>n</jats:italic>, and the other two <jats:inline-formula id=\"j_eqc-2024-0001_ineq_9998\">\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mrow>\n <m:mo stretchy=\"false\">(</m:mo>\n <m:msub>\n <m:mi>a</m:mi>\n <m:mi>n</m:mi>\n </m:msub>\n <m:mo>,</m:mo>\n <m:msub>\n <m:mi>c</m:mi>\n <m:mi>n</m:mi>\n </m:msub>\n <m:mo stretchy=\"false\">)</m:mo>\n </m:mrow>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_eqc-2024-0001_eq_0227.png\" />\n <jats:tex-math>{(a_{n},c_{n})}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula> characterizing the altering reproduction laws. We establish a sequence of transparent limit theorems for the theta-processes with possibly defective reproduction laws. These results may serve as a stepping stone towards incisive general results for the Galton–Watson processes in a varying environment.</jats:p>","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"45 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Galton–Watson Theta-Processes in a Varying Environment\",\"authors\":\"S. 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We establish a sequence of transparent limit theorems for the theta-processes with possibly defective reproduction laws. These results may serve as a stepping stone towards incisive general results for the Galton–Watson processes in a varying environment.</jats:p>\",\"PeriodicalId\":37499,\"journal\":{\"name\":\"Stochastics and Quality Control\",\"volume\":\"45 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Stochastics and Quality Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/eqc-2024-0001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastics and Quality Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/eqc-2024-0001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
我们考虑一类特殊的加尔顿-沃森 Theta 过程，它处于完全由四个参数定义的变化环境中，其中两个参数 ( θ , r ) {(\theta,r)} 在时间 n 上是固定的，另外两个 ( a n , c n ) {(a_{n},c_{n})}表征不断变化的再生产规律。我们为可能存在缺陷的再生产规律的θ过程建立了一系列透明极限定理。这些结果可以作为通向变化环境中加尔顿-沃森过程的精辟一般结果的垫脚石。
Galton–Watson Theta-Processes in a Varying Environment
We consider a special class of Galton–Watson theta-processes in a varying environment fully defined by four parameters, with two of them (θ,r){(\theta,r)} being fixed over time n, and the other two (an,cn){(a_{n},c_{n})} characterizing the altering reproduction laws. We establish a sequence of transparent limit theorems for the theta-processes with possibly defective reproduction laws. These results may serve as a stepping stone towards incisive general results for the Galton–Watson processes in a varying environment.
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