{"title":"Well-posedness for anticipated backward stochastic Schrödinger equations","authors":"Zhang Chen, Li Yang","doi":"10.1080/17442508.2023.2279316","DOIUrl":null,"url":null,"abstract":"AbstractIn this paper, we consider the well-posedness for the anticipated backward stochastic Schrödinger equation in a bounded domain or the whole space Rd, which is associated to a stochastic control problem of nonlinear Schrödinger equations with time delay effect. The approach to establish the existence and uniqueness of adapted solutions are mainly based on the complex Itô's formula, the Galerkin's approximation method and the martingale representation theorem.Keywords: Stochastic Schrödinger equationanticipated backward stochastic differential equationswell-posednessGalerkin's approximation2010 Mathematics Subject Classifications: 60H0560H1560G99 AcknowledgmentsThe authors would like to thank the referees for a careful reading of the manuscript and for a number of useful comments and suggestions for improving the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work is supported by NSFC [grant numbers 11471190 and 11971260].","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":" 1","pages":"0"},"PeriodicalIF":0.8000,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastics-An International Journal of Probability and Stochastic Processes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/17442508.2023.2279316","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
AbstractIn this paper, we consider the well-posedness for the anticipated backward stochastic Schrödinger equation in a bounded domain or the whole space Rd, which is associated to a stochastic control problem of nonlinear Schrödinger equations with time delay effect. The approach to establish the existence and uniqueness of adapted solutions are mainly based on the complex Itô's formula, the Galerkin's approximation method and the martingale representation theorem.Keywords: Stochastic Schrödinger equationanticipated backward stochastic differential equationswell-posednessGalerkin's approximation2010 Mathematics Subject Classifications: 60H0560H1560G99 AcknowledgmentsThe authors would like to thank the referees for a careful reading of the manuscript and for a number of useful comments and suggestions for improving the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work is supported by NSFC [grant numbers 11471190 and 11971260].
期刊介绍：
Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects.
Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly.
In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.
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