{"title":"类稳定过程生成McKean-Vlasov型SPDEs的正则性和灵敏度","authors":"V. Kolokoltsov, M. Troeva","doi":"10.15393/j3.art.2018.5250","DOIUrl":null,"url":null,"abstract":"In this paper we study the sensitivity of nonlinear stochastic differential equations of McKean-Vlasov type generated by stable-like processes. By using the method of stochastic characteristics, we transfer these equations to the non-stochastic equations with random coefficients thus making it possible to use the results obtained for nonlinear PDE of McKean-Vlasov type generated by stable-like processes in the previous works. The motivation for studying sensitivity of nonlinear McKean-Vlasov SPDEs arises naturally from the analysis of the mean-field games with common noise.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"16 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2018-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Regularity and Sensitivity for McKean-Vlasov Type SPDEs Generated by Stable-like Processes\",\"authors\":\"V. Kolokoltsov, M. Troeva\",\"doi\":\"10.15393/j3.art.2018.5250\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we study the sensitivity of nonlinear stochastic differential equations of McKean-Vlasov type generated by stable-like processes. By using the method of stochastic characteristics, we transfer these equations to the non-stochastic equations with random coefficients thus making it possible to use the results obtained for nonlinear PDE of McKean-Vlasov type generated by stable-like processes in the previous works. The motivation for studying sensitivity of nonlinear McKean-Vlasov SPDEs arises naturally from the analysis of the mean-field games with common noise.\",\"PeriodicalId\":41813,\"journal\":{\"name\":\"Problemy Analiza-Issues of Analysis\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2018-08-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Problemy Analiza-Issues of Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15393/j3.art.2018.5250\",\"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":"Problemy Analiza-Issues of Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15393/j3.art.2018.5250","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Regularity and Sensitivity for McKean-Vlasov Type SPDEs Generated by Stable-like Processes
In this paper we study the sensitivity of nonlinear stochastic differential equations of McKean-Vlasov type generated by stable-like processes. By using the method of stochastic characteristics, we transfer these equations to the non-stochastic equations with random coefficients thus making it possible to use the results obtained for nonlinear PDE of McKean-Vlasov type generated by stable-like processes in the previous works. The motivation for studying sensitivity of nonlinear McKean-Vlasov SPDEs arises naturally from the analysis of the mean-field games with common noise.
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