In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale in...In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale inequalities of mixed quasi-martingale Hardy spaces.Moreover,we furnish sufficient conditions for the boundedness ofσ-sublinear operators in these spaces.These findings extend the existing conclusions regarding mixed quasi-martingale Hardy spaces defined with the help of the mixed L_(p)-norm.展开更多
This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
Many complex systems are frequently subject to the influence of uncertain disturbances,which can exert a profound effect on the critical transitions(CTs),potentially resulting in catastrophic consequences.Consequently...Many complex systems are frequently subject to the influence of uncertain disturbances,which can exert a profound effect on the critical transitions(CTs),potentially resulting in catastrophic consequences.Consequently,it is of uttermost importance to provide warnings for noise-induced CTs in various applications.Although capturing certain generic symptoms of transition behaviors from observational and simulated data poses a challenging problem,this work attempts to extract information regarding CTs from simulated data of a Gaussian white noise-induced tri-stable system.Using the extended dynamic mode decomposition(EDMD)algorithm,we initially obtain finite-dimensional approximations of both the stochastic Koopman operator and the generator.Subsequently,the drift parameters and the noise intensity within the system are identified from the simulated data.Utilizing the identified system,the parameter-dependent basin of the unsafe regime(PDBUR)is quantified,enabling data-driven early warning of Gaussian white noise-induced CTs.Finally,an error analysis is carried out to verify the effectiveness of the data-driven results.Our findings may serve as a paradigm for understanding and predicting noise-induced CTs in complex systems based on data.展开更多
针对体系优化存在的体系建模困难、难以量化反映体系效能问题,本文在深入分析武器装备体系结构基础上,通过基于Agent的建模和图示评审技术(graphical evaluation and review technique,GERT)构建具有自学习机制的体系A-GERT网络,实现体...针对体系优化存在的体系建模困难、难以量化反映体系效能问题,本文在深入分析武器装备体系结构基础上,通过基于Agent的建模和图示评审技术(graphical evaluation and review technique,GERT)构建具有自学习机制的体系A-GERT网络,实现体系效能优化。其次,基于矩母函数与梅森公式给出了体系作战链/网任务成功概率和作战效能的计算方法和证明,并在深刻剖析体系组成单元贡献的基础上,借助合作博弈的利益公平分配思想,提出了基于Shapley值的体系组成单元期望贡献评估模型。然后,基于马尔可夫过程理论,提出了基于组成单元贡献的A-GERT网络体系效能优化算法。最后结合实例研究,说明了所提模型的可行性和有效性。展开更多
基金Supported by the National Natural Science Foundation of China(11871195)。
文摘In this article,we conduct a study on mixed quasi-martingale Hardy spaces that are defined by means of the mixed L_(p)-norm.By utilizing Doob’s inequalities,we explore the atomic decomposition and quasi-martingale inequalities of mixed quasi-martingale Hardy spaces.Moreover,we furnish sufficient conditions for the boundedness ofσ-sublinear operators in these spaces.These findings extend the existing conclusions regarding mixed quasi-martingale Hardy spaces defined with the help of the mixed L_(p)-norm.
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金Project supported by the National Natural Science Foundation of China(No.12402033)the National Natural Science Foundation for Distinguished Young Scholars of China(No.52225211)。
文摘Many complex systems are frequently subject to the influence of uncertain disturbances,which can exert a profound effect on the critical transitions(CTs),potentially resulting in catastrophic consequences.Consequently,it is of uttermost importance to provide warnings for noise-induced CTs in various applications.Although capturing certain generic symptoms of transition behaviors from observational and simulated data poses a challenging problem,this work attempts to extract information regarding CTs from simulated data of a Gaussian white noise-induced tri-stable system.Using the extended dynamic mode decomposition(EDMD)algorithm,we initially obtain finite-dimensional approximations of both the stochastic Koopman operator and the generator.Subsequently,the drift parameters and the noise intensity within the system are identified from the simulated data.Utilizing the identified system,the parameter-dependent basin of the unsafe regime(PDBUR)is quantified,enabling data-driven early warning of Gaussian white noise-induced CTs.Finally,an error analysis is carried out to verify the effectiveness of the data-driven results.Our findings may serve as a paradigm for understanding and predicting noise-induced CTs in complex systems based on data.
文摘针对体系优化存在的体系建模困难、难以量化反映体系效能问题,本文在深入分析武器装备体系结构基础上,通过基于Agent的建模和图示评审技术(graphical evaluation and review technique,GERT)构建具有自学习机制的体系A-GERT网络,实现体系效能优化。其次,基于矩母函数与梅森公式给出了体系作战链/网任务成功概率和作战效能的计算方法和证明,并在深刻剖析体系组成单元贡献的基础上,借助合作博弈的利益公平分配思想,提出了基于Shapley值的体系组成单元期望贡献评估模型。然后,基于马尔可夫过程理论,提出了基于组成单元贡献的A-GERT网络体系效能优化算法。最后结合实例研究,说明了所提模型的可行性和有效性。
