{"title":"分数布朗运动驱动的双时标中性随机时滞偏微分方程的平均原理","authors":"Bin Pei, Yong Xu, Min Han","doi":"10.1080/17442508.2023.2258250","DOIUrl":null,"url":null,"abstract":"AbstractWe prove the validity of averaging principles for two-time-scale neutral stochastic delay partial differential equations (NSDPDEs) driven by fractional Brownian motions (fBms) under two-time-scale formulation. Firstly, in the sense of mean-square convergence, we obtain not only the averaging principles for NSDPDEs involving two-time-scale Markov switching with a single weakly recurrent class but also for the case of two-time-scale Markov switching with multiple weakly irreducible classes. Secondly, averaging principles for NSDPDEs driven by fBms with random delay modulated by two-time-scale Markovian switching are established. We proved that there is a limit process in which the fast changing noise is averaged out. The limit process is substantially simpler than that of the original full fast–slow system.Keywords: Averaging principlesneutral stochastic delay partial differential equationsrandom delayfractional Brownian motionstwo-time-scale Markov switching2010 Mathematics Subject Classifications: Primary: 60G22Secondary: 60H15 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingPei's work was partially supported by National Natural Science Foundation of China (NSFC) [grant number 12172285], NSFC-Chongqing [grant number cstc2021jcyj-msxmX0296], Shaanxi Fundamental Science Research Project for Mathematics and Physics [grant number 22JSQ027], Fundamental Research Funds for the Central Universities, Young Talent Fund of the University Association for Science and Technology in Shaanxi, China. Xu's work was partially supported by NSFC [grant number 12072264], and NSFC Key International (Regional) Joint Research Program [grant number 12120101002].","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Averaging principles for two-time-scale neutral stochastic delay partial differential equations driven by fractional Brownian motions\",\"authors\":\"Bin Pei, Yong Xu, Min Han\",\"doi\":\"10.1080/17442508.2023.2258250\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"AbstractWe prove the validity of averaging principles for two-time-scale neutral stochastic delay partial differential equations (NSDPDEs) driven by fractional Brownian motions (fBms) under two-time-scale formulation. Firstly, in the sense of mean-square convergence, we obtain not only the averaging principles for NSDPDEs involving two-time-scale Markov switching with a single weakly recurrent class but also for the case of two-time-scale Markov switching with multiple weakly irreducible classes. Secondly, averaging principles for NSDPDEs driven by fBms with random delay modulated by two-time-scale Markovian switching are established. We proved that there is a limit process in which the fast changing noise is averaged out. The limit process is substantially simpler than that of the original full fast–slow system.Keywords: Averaging principlesneutral stochastic delay partial differential equationsrandom delayfractional Brownian motionstwo-time-scale Markov switching2010 Mathematics Subject Classifications: Primary: 60G22Secondary: 60H15 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingPei's work was partially supported by National Natural Science Foundation of China (NSFC) [grant number 12172285], NSFC-Chongqing [grant number cstc2021jcyj-msxmX0296], Shaanxi Fundamental Science Research Project for Mathematics and Physics [grant number 22JSQ027], Fundamental Research Funds for the Central Universities, Young Talent Fund of the University Association for Science and Technology in Shaanxi, China. Xu's work was partially supported by NSFC [grant number 12072264], and NSFC Key International (Regional) Joint Research Program [grant number 12120101002].\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/17442508.2023.2258250\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/17442508.2023.2258250","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Averaging principles for two-time-scale neutral stochastic delay partial differential equations driven by fractional Brownian motions
AbstractWe prove the validity of averaging principles for two-time-scale neutral stochastic delay partial differential equations (NSDPDEs) driven by fractional Brownian motions (fBms) under two-time-scale formulation. Firstly, in the sense of mean-square convergence, we obtain not only the averaging principles for NSDPDEs involving two-time-scale Markov switching with a single weakly recurrent class but also for the case of two-time-scale Markov switching with multiple weakly irreducible classes. Secondly, averaging principles for NSDPDEs driven by fBms with random delay modulated by two-time-scale Markovian switching are established. We proved that there is a limit process in which the fast changing noise is averaged out. The limit process is substantially simpler than that of the original full fast–slow system.Keywords: Averaging principlesneutral stochastic delay partial differential equationsrandom delayfractional Brownian motionstwo-time-scale Markov switching2010 Mathematics Subject Classifications: Primary: 60G22Secondary: 60H15 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingPei's work was partially supported by National Natural Science Foundation of China (NSFC) [grant number 12172285], NSFC-Chongqing [grant number cstc2021jcyj-msxmX0296], Shaanxi Fundamental Science Research Project for Mathematics and Physics [grant number 22JSQ027], Fundamental Research Funds for the Central Universities, Young Talent Fund of the University Association for Science and Technology in Shaanxi, China. Xu's work was partially supported by NSFC [grant number 12072264], and NSFC Key International (Regional) Joint Research Program [grant number 12120101002].