{"title":"圆柱维纳过程驱动的巴拿赫空间中的随机微分方程","authors":"Badri Mamporia","doi":"10.1016/j.trmi.2016.10.003","DOIUrl":null,"url":null,"abstract":"<div><p>Generalized stochastic integral from predictable operator-valued random process with respect to a cylindrical Wiener process in an arbitrary Banach space is defined. The question of existence of the stochastic integral in a Banach space is reduced to the problem of decomposability of the generalized random element. The sufficient condition of existence of the stochastic integral in terms of <span><math><mi>p</mi></math></span>-absolutely summing operators is given. The stochastic differential equation for generalized random processes is considered and existence and uniqueness of the solution is developed. As a consequence, the corresponding results of the stochastic differential equations in an arbitrary Banach space are given.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2017-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2016.10.003","citationCount":"0","resultStr":"{\"title\":\"Stochastic differential equations in a Banach space driven by the cylindrical Wiener process\",\"authors\":\"Badri Mamporia\",\"doi\":\"10.1016/j.trmi.2016.10.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Generalized stochastic integral from predictable operator-valued random process with respect to a cylindrical Wiener process in an arbitrary Banach space is defined. The question of existence of the stochastic integral in a Banach space is reduced to the problem of decomposability of the generalized random element. The sufficient condition of existence of the stochastic integral in terms of <span><math><mi>p</mi></math></span>-absolutely summing operators is given. The stochastic differential equation for generalized random processes is considered and existence and uniqueness of the solution is developed. As a consequence, the corresponding results of the stochastic differential equations in an arbitrary Banach space are given.</p></div>\",\"PeriodicalId\":43623,\"journal\":{\"name\":\"Transactions of A Razmadze Mathematical Institute\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2017-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.trmi.2016.10.003\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of A Razmadze Mathematical Institute\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2346809216300381\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of A Razmadze Mathematical Institute","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2346809216300381","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Stochastic differential equations in a Banach space driven by the cylindrical Wiener process
Generalized stochastic integral from predictable operator-valued random process with respect to a cylindrical Wiener process in an arbitrary Banach space is defined. The question of existence of the stochastic integral in a Banach space is reduced to the problem of decomposability of the generalized random element. The sufficient condition of existence of the stochastic integral in terms of -absolutely summing operators is given. The stochastic differential equation for generalized random processes is considered and existence and uniqueness of the solution is developed. As a consequence, the corresponding results of the stochastic differential equations in an arbitrary Banach space are given.