This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the n...This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.展开更多
The paper is devoted to investigating the weighted variation inequalities for onesided Calderon-Zygmund singular integral commutators. To be precise, we establish weighted variation inequalities for commutators genera...The paper is devoted to investigating the weighted variation inequalities for onesided Calderon-Zygmund singular integral commutators. To be precise, we establish weighted variation inequalities for commutators generated by one-sided Calderon-Zygmund singular integral operators and Lipschitz functions. Moreover, using extrapolation of one-sided weights,the boundedness of the variation operators for these commutators is established on one-sided Triebel-Lizorkin spaces.展开更多
In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is as...In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.展开更多
In this paper, we establish the weighted <span style="white-space:nowrap;">L<sup>p</sup> <span style="white-space:nowrap;">(1 < p < ∞) boundedness of variation operat...In this paper, we establish the weighted <span style="white-space:nowrap;">L<sup>p</sup> <span style="white-space:nowrap;">(1 < p < ∞) boundedness of variation operator for the commutators generated by one-sided Calderón-Zygmund singular integrals with Lipschitz functions.展开更多
This paper investigates the problem of observer design for a class of control systems.Different from current works,the nonlinear functions in the system only satisfy the property of the one-sided Lipschitz(OSL)conditi...This paper investigates the problem of observer design for a class of control systems.Different from current works,the nonlinear functions in the system only satisfy the property of the one-sided Lipschitz(OSL)condition but not quadratic inner-boundedness(QIB).Moreover,the case where the OSL constant is negative is specially investigated.Firstly,a full-order observer is constructed for the original system.Then,a reduced-order observer is also designed by using the decomposition method.The advantage and effectiveness of the proposed design scheme are shown in a numerical simulation.展开更多
In this paper, we continue studying the so called best m-term one-sided approximation and Greedy-liked one-sided ap- proximation by the trigonometric polynomials. The asymptotic estimations of the best m-terms one-sid...In this paper, we continue studying the so called best m-term one-sided approximation and Greedy-liked one-sided ap- proximation by the trigonometric polynomials. The asymptotic estimations of the best m-terms one-sided approximation by the trigonometric polynomials on some classes of Besov spaces in the metricLp(Td(1≤p≤∞ are given.展开更多
This paper investigates the finite-time H_(∞)control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties.Using the one-sided Lipschitz and quadratically inner-bounded conditi...This paper investigates the finite-time H_(∞)control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties.Using the one-sided Lipschitz and quadratically inner-bounded conditions,the authors derive less conservative criterion for the controller design and observer design.A new criterion is proposed to ensure the closed-loop system is finite-time bounded(FTB).The sufficient conditions are established to ensure the closed-loop system is H_(∞)finite-time bounded(H_(∞)FTB)in terms of matrix inequalities.The controller gains and observer gains are given.A numerical example is provided to demonstrate the effectiveness of the proposed results.展开更多
In this paper, we characterize the sharp boundedness of the one-sided fractional maximal function for one-weight and two-weight inequalities. Also a new two-weight testing condition for the one-sided fractional maxima...In this paper, we characterize the sharp boundedness of the one-sided fractional maximal function for one-weight and two-weight inequalities. Also a new two-weight testing condition for the one-sided fractional maximal function is introduced extending the work of Martin-Reyes and de la Torre. Improving some extrapolation result for the one-sided case, we get weak sharp bounded estimates for one-sided fractional maximal function and weak and strong sharp bounded estimates for one-sided fractional integral.展开更多
We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition...We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works.展开更多
In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coef...In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.展开更多
In this study, we investigate the tail probability of the discounted aggregate claim sizes in a dependent risk model. In this model, the claim sizes are observed to follow a one-sided linear process with independent a...In this study, we investigate the tail probability of the discounted aggregate claim sizes in a dependent risk model. In this model, the claim sizes are observed to follow a one-sided linear process with independent and identically distributed innovations. Investment return is described as a general stochastic process with c`adl`ag paths. In the case of heavy-tailed innovation distributions, we are able to derive some asymptotic estimates for tail probability and to provide some asymptotic upper bounds to improve the applicability of our study.展开更多
In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the...In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the norm Lp （1 ≤ p ≤ ∞） of multiplier function classes and the corresponding m-term Greedy-liked one-sided trigonometric approximation results.展开更多
We give a necessary and sufficient condition for the fundamental group homomorphism of a map between CW-complexes(manifolds) to induce partial homology equivalences. As applications, we obtain characterizations of fun...We give a necessary and sufficient condition for the fundamental group homomorphism of a map between CW-complexes(manifolds) to induce partial homology equivalences. As applications, we obtain characterizations of fundamental groups of homology spheres and Moore manifolds. Moreover, a classification of one-sided h-cobordism of manifolds up to diffeomorphisms is obtained, based on Quillen's plus construction with Whitehead torsions.展开更多
We investigate the branching structure coded by the excursion above zero of a spectrally positive Levy process. The main idea is to identify the level of the Levy excursion as the time and count the number of jumps up...We investigate the branching structure coded by the excursion above zero of a spectrally positive Levy process. The main idea is to identify the level of the Levy excursion as the time and count the number of jumps upcrossing the level. By regarding the size of a jump as the birth site of a particle, we construct a branching particle system in which the particles undergo nonlocal branchings and deterministic spatial motions to the left on the positive half line. A particle is removed from the system as soon as it reaches the origin. Then a measure-valued Borel right Markov process can be defined as the counting measures of the particle system. Its total mass evolves according to a Crump- Mode-Jagers （CMJ） branching process and its support represents the residual life times of those existing particles. A similar result for spectrally negative Levy process is established by a time reversal approach. Properties of the measure- valued processes can be studied via the excursions for the corresponding Levy processes.展开更多
This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes th...This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes the results in [Li, T. and Yu, L., One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws, To appear in Journal de Mathematiques Pures et Appliquees, 2016.] for a class of strictly hyperbolic systems of conservation laws.展开更多
This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping...This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping using the concept of‘return time’is also proposed.The controller design relies on the solution of Linear Matrix Inequalities(LMIs)and hence is compu-tationally efficient.The proposed control law is linear in states,and thus the implementation is often straightforward.To illustrate the capability and simplicity of the proposed theory,three design examples are included.展开更多
The purpose of this paper is to show that for one-sided symbolic systems,there exists an uncountable distributionally scrambled set contained in the set of proper positive upper Banach density recurrent points.
In this paper, we study the stability of a class of conformable fractional-order systems using the Lyapunov function. We assume that the nonlinear part of the system satisfies the one-sided Lipschitz condition and the...In this paper, we study the stability of a class of conformable fractional-order systems using the Lyapunov function. We assume that the nonlinear part of the system satisfies the one-sided Lipschitz condition and the quadratic inner-bounded condition. We provide some sufficient conditions that ensure the asymptotic stability of the system. Furthermore, we present the construction of a feedback stabilizing controller for conformable fractional bilinear systems.展开更多
This paper addresses the practical stabilization problem for a class of one-sided Lipschitz nonlinear time delay systems with external disturbances.In case there is no perturbation,the exponential convergence of the o...This paper addresses the practical stabilization problem for a class of one-sided Lipschitz nonlinear time delay systems with external disturbances.In case there is no perturbation,the exponential convergence of the observer was confirmed.When external disturbances appear in the system,a separation principle is established,and the authors show that the closed loop system is exponentially practical stable.By choosing a suitable Lyapunov-Krasovskii functional,the authors derive new sufficient conditions to guarantee the exponential stability of the systems.Finally,a physical model is performed to prove the efficiency and applicability of the suggested approach.展开更多
In this paper we propose an absolute error loss EB estimator for parameter of one-side truncation distribution families. Under some conditions we have proved that the convergence rates of its Bayes risk is o, where 0&...In this paper we propose an absolute error loss EB estimator for parameter of one-side truncation distribution families. Under some conditions we have proved that the convergence rates of its Bayes risk is o, where 0<λ,r≤1,Mn≤lnln n (for large n),Mn→∞ as n→∞.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12471394,12371417)Natural Science Foundation of Changsha(No.kq2502101)。
文摘This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.
基金Supported by the National Natural Science Foundation of China (Grant No. 12361019)the Natural Science Foundation of Xinjiang Uygur Autonomous Region (Grant No. 2021D01C463)YiLi Normal University’s“High-level Talents” Program of Academic Integrity (Grant No. YSXSJS22001)。
文摘The paper is devoted to investigating the weighted variation inequalities for onesided Calderon-Zygmund singular integral commutators. To be precise, we establish weighted variation inequalities for commutators generated by one-sided Calderon-Zygmund singular integral operators and Lipschitz functions. Moreover, using extrapolation of one-sided weights,the boundedness of the variation operators for these commutators is established on one-sided Triebel-Lizorkin spaces.
基金Supported by the National Natural Science Foundation of China(11671375 and 11471303)Natural Science Foundation of Anhui Provincial Education Department(KJ2017A171)
文摘In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.
文摘In this paper, we establish the weighted <span style="white-space:nowrap;">L<sup>p</sup> <span style="white-space:nowrap;">(1 < p < ∞) boundedness of variation operator for the commutators generated by one-sided Calderón-Zygmund singular integrals with Lipschitz functions.
基金the National Natural Science Foundation of China(No.61403267)the China Postdoctoral Science Foundation(No.2017M611903)。
文摘This paper investigates the problem of observer design for a class of control systems.Different from current works,the nonlinear functions in the system only satisfy the property of the one-sided Lipschitz(OSL)condition but not quadratic inner-boundedness(QIB).Moreover,the case where the OSL constant is negative is specially investigated.Firstly,a full-order observer is constructed for the original system.Then,a reduced-order observer is also designed by using the decomposition method.The advantage and effectiveness of the proposed design scheme are shown in a numerical simulation.
文摘In this paper, we continue studying the so called best m-term one-sided approximation and Greedy-liked one-sided ap- proximation by the trigonometric polynomials. The asymptotic estimations of the best m-terms one-sided approximation by the trigonometric polynomials on some classes of Besov spaces in the metricLp(Td(1≤p≤∞ are given.
基金supported by the Natural Science Foundation of Tianjin under Grant No.18JCYBJC88000.
文摘This paper investigates the finite-time H_(∞)control problem for a class of nonlinear discrete-time one-sided Lipschitz systems with uncertainties.Using the one-sided Lipschitz and quadratically inner-bounded conditions,the authors derive less conservative criterion for the controller design and observer design.A new criterion is proposed to ensure the closed-loop system is finite-time bounded(FTB).The sufficient conditions are established to ensure the closed-loop system is H_(∞)finite-time bounded(H_(∞)FTB)in terms of matrix inequalities.The controller gains and observer gains are given.A numerical example is provided to demonstrate the effectiveness of the proposed results.
文摘In this paper, we characterize the sharp boundedness of the one-sided fractional maximal function for one-weight and two-weight inequalities. Also a new two-weight testing condition for the one-sided fractional maximal function is introduced extending the work of Martin-Reyes and de la Torre. Improving some extrapolation result for the one-sided case, we get weak sharp bounded estimates for one-sided fractional maximal function and weak and strong sharp bounded estimates for one-sided fractional integral.
基金Supported by National Natural Science Foundation of China(Grant No.11371362)the Fundamental Research Funds for the Central Universities(Grant No.2012QNA36)
文摘We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works.
基金supported by the National Natural Science Foundation of China(Nos.11671113,12071101).
文摘In this paper,we consider the stochastic differential equations with piecewise continuous arguments(SDEPCAs)in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition.Since the delay term t-[t]of SDEPCAs is not continuous and differentiable,the variable substitution method is not suitable.To overcome this dificulty,we adopt new techniques to prove the boundedness of the exact solution and the numerical solution.It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of L'(q≥2).We obtain the convergence order with some additional conditions.An example is presented to illustrate the analytical theory.
基金supported by National Natural Science Foundation of China (Grant No. 71501100)the Open Project of Jiangsu Key Laboratory of Financial Engineering (Grant No. NSK2015-02)+1 种基金supported by National Natural Science Foundation of China (Grant No. 71271042)the stage results of the Major Bidding Project of the Chinese National Social Science Foundation (Grant No. 17ZDA072)
文摘In this study, we investigate the tail probability of the discounted aggregate claim sizes in a dependent risk model. In this model, the claim sizes are observed to follow a one-sided linear process with independent and identically distributed innovations. Investment return is described as a general stochastic process with c`adl`ag paths. In the case of heavy-tailed innovation distributions, we are able to derive some asymptotic estimates for tail probability and to provide some asymptotic upper bounds to improve the applicability of our study.
基金Supported by National Natural Science Foundation of China (Grant No. 10771016) supported by Shandong Agricultural University Youth Foundation
文摘In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the norm Lp （1 ≤ p ≤ ∞） of multiplier function classes and the corresponding m-term Greedy-liked one-sided trigonometric approximation results.
基金supported by National Natural Science Foundation of China(Grand No.10901151)RDF-13-02-08 of Xi’an Jiaotong-Liverpool University
文摘We give a necessary and sufficient condition for the fundamental group homomorphism of a map between CW-complexes(manifolds) to induce partial homology equivalences. As applications, we obtain characterizations of fundamental groups of homology spheres and Moore manifolds. Moreover, a classification of one-sided h-cobordism of manifolds up to diffeomorphisms is obtained, based on Quillen's plus construction with Whitehead torsions.
基金Hui He wanted to thank Concordia University for his pleasant stay at Montreal where this work was done. The authors would like to thank Professor Wenming Hong for his enlightening discussion. They also would like to thank Amaury Lambert for suggesting the time reversal treatment of the model in Section 5. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11201030, 11371061）, the Fundamental Research Funds for the Central Universities （2013YB59）, and the Natural Sciences and Engineering Research Council of Canada.
文摘We investigate the branching structure coded by the excursion above zero of a spectrally positive Levy process. The main idea is to identify the level of the Levy excursion as the time and count the number of jumps upcrossing the level. By regarding the size of a jump as the birth site of a particle, we construct a branching particle system in which the particles undergo nonlocal branchings and deterministic spatial motions to the left on the positive half line. A particle is removed from the system as soon as it reaches the origin. Then a measure-valued Borel right Markov process can be defined as the counting measures of the particle system. Its total mass evolves according to a Crump- Mode-Jagers （CMJ） branching process and its support represents the residual life times of those existing particles. A similar result for spectrally negative Levy process is established by a time reversal approach. Properties of the measure- valued processes can be studied via the excursions for the corresponding Levy processes.
基金supported by the National Natural Science Foundation of China(No.11501122)
文摘This paper proves the local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws with characteristics with constant multiplicity. This generalizes the results in [Li, T. and Yu, L., One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws, To appear in Journal de Mathematiques Pures et Appliquees, 2016.] for a class of strictly hyperbolic systems of conservation laws.
文摘This work addresses the reference tracking problem for uncertain systems with quasi one-sided Lipschitz nonlinearity.The uncertainty is assumed to be of a norm bound parametric type.Moreover,transient response shaping using the concept of‘return time’is also proposed.The controller design relies on the solution of Linear Matrix Inequalities(LMIs)and hence is compu-tationally efficient.The proposed control law is linear in states,and thus the implementation is often straightforward.To illustrate the capability and simplicity of the proposed theory,three design examples are included.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11661054 and 11261039)
文摘The purpose of this paper is to show that for one-sided symbolic systems,there exists an uncountable distributionally scrambled set contained in the set of proper positive upper Banach density recurrent points.
文摘In this paper, we study the stability of a class of conformable fractional-order systems using the Lyapunov function. We assume that the nonlinear part of the system satisfies the one-sided Lipschitz condition and the quadratic inner-bounded condition. We provide some sufficient conditions that ensure the asymptotic stability of the system. Furthermore, we present the construction of a feedback stabilizing controller for conformable fractional bilinear systems.
文摘This paper addresses the practical stabilization problem for a class of one-sided Lipschitz nonlinear time delay systems with external disturbances.In case there is no perturbation,the exponential convergence of the observer was confirmed.When external disturbances appear in the system,a separation principle is established,and the authors show that the closed loop system is exponentially practical stable.By choosing a suitable Lyapunov-Krasovskii functional,the authors derive new sufficient conditions to guarantee the exponential stability of the systems.Finally,a physical model is performed to prove the efficiency and applicability of the suggested approach.
文摘In this paper we propose an absolute error loss EB estimator for parameter of one-side truncation distribution families. Under some conditions we have proved that the convergence rates of its Bayes risk is o, where 0<λ,r≤1,Mn≤lnln n (for large n),Mn→∞ as n→∞.
