Well-posedness for anticipated backward stochastic Schrödinger equations

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2023-11-09 DOI:10.1080/17442508.2023.2279316

Zhang Chen, Li Yang

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].

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预期倒向随机Schrödinger方程的适定性

摘要本文研究了具有时滞效应的非线性Schrödinger方程的随机控制问题，研究了有界域或全空间Rd上期望倒向随机Schrödinger方程的适定性问题。建立自适应解的存在唯一性的方法主要是基于复Itô公式、伽辽金近似法和鞅表示定理。关键词:随机Schrödinger方程;预期后向随机微分方程;泛波完备性;伽辽金近似;2010数学学科分类:60H0560H1560G99致谢作者感谢审稿人对本文的认真阅读，并对本文的改进提出了许多有用的意见和建议。披露声明作者未报告潜在的利益冲突。本研究由国家自然科学基金资助[批准号:11471190和11971260]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

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.