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
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.
