{"title":"随机控制迷你课程","authors":"Qi Lu, Xu Zhang","doi":"10.1142/9789813276154_0004","DOIUrl":null,"url":null,"abstract":"This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties in the study of controllability and optimal control problems for these sort of equations. In particular, we will show by some examples that both the formulation of stochastic control problems and the tools to solve them may differ considerably from their deterministic counterpart.","PeriodicalId":292296,"journal":{"name":"Series in Contemporary Applied Mathematics","volume":"35 9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"A Mini-Course on Stochastic Control\",\"authors\":\"Qi Lu, Xu Zhang\",\"doi\":\"10.1142/9789813276154_0004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties in the study of controllability and optimal control problems for these sort of equations. In particular, we will show by some examples that both the formulation of stochastic control problems and the tools to solve them may differ considerably from their deterministic counterpart.\",\"PeriodicalId\":292296,\"journal\":{\"name\":\"Series in Contemporary Applied Mathematics\",\"volume\":\"35 9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-12-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Series in Contemporary Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/9789813276154_0004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Series in Contemporary Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/9789813276154_0004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties in the study of controllability and optimal control problems for these sort of equations. In particular, we will show by some examples that both the formulation of stochastic control problems and the tools to solve them may differ considerably from their deterministic counterpart.
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