In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; ...In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; partitioning estimation; strong convergence;φ-mixing sequences.展开更多
In this paper, we study the strong consistency and convergence rate for modified partitioning estimation of regression function under samples that are ψ-mixing with identically distribution.
In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent(NOD) random variables are investigated. Let {X, n ≥ 1}be a sequence of NOD random variables. The results...In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent(NOD) random variables are investigated. Let {X, n ≥ 1}be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.展开更多
This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang (2005) prop...This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang (2005) proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.展开更多
In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our me...In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our method requires only to compute one projection onto the feasible set per iteration and without any linesearch procedure or additional projections as well as does not need to the prior knowledge of the Lipschitz constant and the sequentially weakly continuity of the variational inequality mapping.A strong convergence is established for the proposed method to a solution of a variational inequality problem under certain mild assumptions.Finally,we give some numerical experiments illustrating the performance of the proposed method for variational inequality problems.展开更多
In this paper, by the three series theorem of m-negatively associated(m-NA,in short) random variables and the truncation method of random variables, we mainly investigated the strong convergence properties for partial...In this paper, by the three series theorem of m-negatively associated(m-NA,in short) random variables and the truncation method of random variables, we mainly investigated the strong convergence properties for partial sums of m-NA random variables.In addition, the Khintchine-Kolmogorov convergence theorem and Kolmogorov-type strong law of large numbers for m-NA random variables are also obtained. The results obtained in the paper generalize some corresponding ones for independent random variables and some dependent random variables.展开更多
The purpose of this article is to introduce a class of total quasi-Ф- asymptotically nonexpansive nonself mappings. Strong convergence theorems for common fixed points of a countable family of total quasi-Ф-asymptot...The purpose of this article is to introduce a class of total quasi-Ф- asymptotically nonexpansive nonself mappings. Strong convergence theorems for common fixed points of a countable family of total quasi-Ф-asymptotically nonexpan- sive mappings are established in the framework of Banach spaces based on modified Halpern and Mann-type iteration algorithm. The main results presented in this article extend and improve the corresponding results of many authors.展开更多
In this paper,we study an extragradient algorithm for approximating solutions of quasi-equilibrium problems in Banach spaces.We prove strong convergence of the sequence generated by the extragradient method to a solut...In this paper,we study an extragradient algorithm for approximating solutions of quasi-equilibrium problems in Banach spaces.We prove strong convergence of the sequence generated by the extragradient method to a solution of the quasi-equilibrium problem.展开更多
The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove str...The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces.展开更多
In this paper,we study the strong convergence of a jump-adapted implicit Milstein method for a class of jump-diffusion stochastic differential equations with non-globally Lipschitz drift coefficients.Compared with the...In this paper,we study the strong convergence of a jump-adapted implicit Milstein method for a class of jump-diffusion stochastic differential equations with non-globally Lipschitz drift coefficients.Compared with the regular methods,the jump-adapted methods can significantly reduce the complexity of higher order methods,which makes them easily implementable for scenario simulation.However,due to the fact that jump-adapted time discretization is path dependent and the stepsize is not uniform,this makes the numerical analysis of jump-adapted methods much more involved,especially in the non-globally Lipschitz setting.We provide a rigorous strong convergence analysis of the considered jump-adapted implicit Milstein method by developing some novel analysis techniques and optimal rate with order one is also successfully recovered.Numerical experiments are carried out to verify the theoretical findings.展开更多
In this paper, we consider hybrid algorithms for finding common elements of the set of common fixed points of two families quasi-C-non-expansive mappings and the set of solutions of an equilibrium problem. We establis...In this paper, we consider hybrid algorithms for finding common elements of the set of common fixed points of two families quasi-C-non-expansive mappings and the set of solutions of an equilibrium problem. We establish strong convergence theorems of common elements in uniformly smooth and strictly convex Banach spaces with the property (K).展开更多
The purpose of this article is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-φ-asymptotically nonexpansive mappings.Its results hold in reflexive,stric...The purpose of this article is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-φ-asymptotically nonexpansive mappings.Its results hold in reflexive,strictly convex,smooth Banach spaces with the property(K).The results of this paper improve and extend recent some relative results.展开更多
In this paper,we investigate the mean-square convergence of the split-step q-scheme for nonlinear stochastic differential equations with jumps.Under some standard assumptions,we rigorously prove that the strong rate o...In this paper,we investigate the mean-square convergence of the split-step q-scheme for nonlinear stochastic differential equations with jumps.Under some standard assumptions,we rigorously prove that the strong rate of convergence of the splitstep q-scheme in strong sense is one half.Some numerical experiments are carried out to assert our theoretical result.展开更多
A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty ...A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991).展开更多
In this paper,we consider the Euler-Maruyama method for a class of stochastic Volterra integral equations(SVIEs).It is known that the strong convergence order of the EulerMaruyama method is 12.However,the strong super...In this paper,we consider the Euler-Maruyama method for a class of stochastic Volterra integral equations(SVIEs).It is known that the strong convergence order of the EulerMaruyama method is 12.However,the strong superconvergence order 1 can be obtained for a class of SVIEs if the kernelsσi(t,t)=0 for i=1 and 2;otherwise,the strong convergence order is 12.Moreover,the theoretical results are illustrated by some numerical examples.展开更多
We consider a nonlinear stochastic Volterra integral equation with time-dependent delay and the corresponding Euler-Maruyama method in this paper.Strong convergence rate(at fixed point)of the corresponding Euler-Maruy...We consider a nonlinear stochastic Volterra integral equation with time-dependent delay and the corresponding Euler-Maruyama method in this paper.Strong convergence rate(at fixed point)of the corresponding Euler-Maruyama method is obtained when coefficients f and g both satisfy local Lipschitz and linear growth conditions.An example is provided to interpret our conclusions.Our result generalizes and improves the conclusion in[J.Gao,H.Liang,S.Ma,Strong convergence of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations with constant delay,Appl.Math.Comput.,348(2019)385-398.]展开更多
This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations(SPDEs)with multiplicative noise.The nonlinearity in the diffusion term of the...This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations(SPDEs)with multiplicative noise.The nonlinearity in the diffusion term of the SPDEs is assumed to be globally Lipschitz and the nonlinearity in the drift term is only assumed to satisfy a one-sided Lipschitz condition.These assumptions are the same ones as the cases where numerical methods for general nonlinear stochastic ordinary differential equations(SODEs)under“minimum assumptions”were studied.As a result,the semilinear SPDEs considered in this paper are a direct generalization of these nonlinear SODEs.There are several difficulties which need to be overcome for this generalization.First,obviously the spatial discretization,which does not appear in the SODE case,adds an extra layer of difficulty.It turns out a spatial discretization must be designed to guarantee certain properties for the numerical scheme and its stiffness matrix.In this paper we use a finite element interpolation technique to discretize the nonlinear drift term.Second,in order to prove the strong convergence of the proposed fully discrete finite element method,stability estimates for higher order moments of the H1-seminorm of the numerical solution must be established,which are difficult and delicate.A judicious combination of the properties of the drift and diffusion terms and some nontrivial techniques is used in this paper to achieve the goal.Finally,stability estimates for the second and higher order moments of the L^(2)-norm of the numerical solution are also difficult to obtain due to the fact that the mass matrix may not be diagonally dominant.This is done by utilizing the interpolation theory and the higher moment estimates for the H1-seminorm of the numerical solution.After overcoming these difficulties,it is proved that the proposed fully discrete finite element method is convergent in strong norms with nearly optimal rates of convergence.Numerical experiment results are also presented to validate the theoretical results and to demonstrate the efficiency of the proposed numerical method.展开更多
In this paper,we revisit the Nested Stochastic Simulation Algorithm(NSSA)for stochastic chemical reacting networks by first proving its strong convergence.We then study a speed up of the algorithm by using the explici...In this paper,we revisit the Nested Stochastic Simulation Algorithm(NSSA)for stochastic chemical reacting networks by first proving its strong convergence.We then study a speed up of the algorithm by using the explicit Tau-Leaping method as the Inner solver to approximate invariant measures of fast processes,for which strong error estimates can also be obtained.Numerical experiments are presented to demonstrate the validity of our analysis.展开更多
The purpose of this paper is to introduce a split generalized mixed equi- librium problem (SGMEP) and consider some iterative sequences to find a solution of the generalized mixed equilibrium problem such that its i...The purpose of this paper is to introduce a split generalized mixed equi- librium problem (SGMEP) and consider some iterative sequences to find a solution of the generalized mixed equilibrium problem such that its image un- der a given bounded linear operator is a solution of another generalized mixed equilibrium problem. We obtain some weak and strong convergence theorems.展开更多
In this paper, strong summability of Cesaro means (of critical order) of Fourier-Laplace series on unit sphere is discussed. The Pointwise convergence conditions are established. The results of this paper are anal-ogo...In this paper, strong summability of Cesaro means (of critical order) of Fourier-Laplace series on unit sphere is discussed. The Pointwise convergence conditions are established. The results of this paper are anal-ogous to those of single and multiple Fourier series.展开更多
基金Supported by the Science Development Foundation of HFUT(041002F)
文摘In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; partitioning estimation; strong convergence;φ-mixing sequences.
基金The Science Research Fundation (041002F) of Hefei University of Technology.
文摘In this paper, we study the strong consistency and convergence rate for modified partitioning estimation of regression function under samples that are ψ-mixing with identically distribution.
基金Supported by the National Natural Science Foundation of China(11671012,11501004,11501005)the Natural Science Foundation of Anhui Province(1508085J06)+2 种基金the Key Projects for Academic Talent of Anhui Province(gxbj ZD2016005)the Quality Engineering Project of Anhui Province(2016jyxm0047)the Graduate Academic Innovation Research Project of Anhui University(yfc100004)
文摘In the paper, the strong convergence properties for two different weighted sums of negatively orthant dependent(NOD) random variables are investigated. Let {X, n ≥ 1}be a sequence of NOD random variables. The results obtained in the paper generalize the corresponding ones for i.i.d. random variables and identically distributed NA random variables to the case of NOD random variables, which are stochastically dominated by a random variable X. As a byproduct, the Marcinkiewicz-Zygmund type strong law of large numbers for NOD random variables is also obtained.
基金supported by the National Natural Science Funds for Distinguished Young Scholar (70825004)National Natural Science Foundation of China (NSFC) (10731010 and 10628104)+3 种基金the National Basic Research Program (2007CB814902)Creative Research Groups of China (10721101)Leading Academic Discipline Program, the 10th five year plan of 211 Project for Shanghai University of Finance and Economics211 Project for Shanghai University of Financeand Economics (the 3rd phase)
文摘This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang (2005) proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.
基金funded by National University ofCivil Engineering(NUCE)under grant number 15-2020/KHXD-TD。
文摘In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our method requires only to compute one projection onto the feasible set per iteration and without any linesearch procedure or additional projections as well as does not need to the prior knowledge of the Lipschitz constant and the sequentially weakly continuity of the variational inequality mapping.A strong convergence is established for the proposed method to a solution of a variational inequality problem under certain mild assumptions.Finally,we give some numerical experiments illustrating the performance of the proposed method for variational inequality problems.
基金Supported by the Natural Science Foundation of Anhui Province(1508085J06) the Key Projects for Academic Talent of Anhui Province(gxbj ZD2016005) the Students Innovative Training Project of Anhui University(201610357001)
文摘In this paper, by the three series theorem of m-negatively associated(m-NA,in short) random variables and the truncation method of random variables, we mainly investigated the strong convergence properties for partial sums of m-NA random variables.In addition, the Khintchine-Kolmogorov convergence theorem and Kolmogorov-type strong law of large numbers for m-NA random variables are also obtained. The results obtained in the paper generalize some corresponding ones for independent random variables and some dependent random variables.
基金Scientific Research Fund(2011JYZ010)of Science Technology Department of Sichuan ProvinceScientific Research Fund(11ZA172 and 12ZB345)of Sichuan Provincial Education Department
文摘The purpose of this article is to introduce a class of total quasi-Ф- asymptotically nonexpansive nonself mappings. Strong convergence theorems for common fixed points of a countable family of total quasi-Ф-asymptotically nonexpan- sive mappings are established in the framework of Banach spaces based on modified Halpern and Mann-type iteration algorithm. The main results presented in this article extend and improve the corresponding results of many authors.
文摘In this paper,we study an extragradient algorithm for approximating solutions of quasi-equilibrium problems in Banach spaces.We prove strong convergence of the sequence generated by the extragradient method to a solution of the quasi-equilibrium problem.
文摘The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces.
基金supported by the National Natural Science Foundation of China(Grant Nos.11901565,12071261,11831010,11871068)by the Science Challenge Project(No.TZ2018001)by National Key R&D Plan of China(Grant No.2018YFA0703900).
文摘In this paper,we study the strong convergence of a jump-adapted implicit Milstein method for a class of jump-diffusion stochastic differential equations with non-globally Lipschitz drift coefficients.Compared with the regular methods,the jump-adapted methods can significantly reduce the complexity of higher order methods,which makes them easily implementable for scenario simulation.However,due to the fact that jump-adapted time discretization is path dependent and the stepsize is not uniform,this makes the numerical analysis of jump-adapted methods much more involved,especially in the non-globally Lipschitz setting.We provide a rigorous strong convergence analysis of the considered jump-adapted implicit Milstein method by developing some novel analysis techniques and optimal rate with order one is also successfully recovered.Numerical experiments are carried out to verify the theoretical findings.
基金Supported by the National Natural Science Foundation of China (No. 10771050)Scientific Research Program Funded by Shaanxi Provincial Education Department (No. 11JK0486)
文摘In this paper, we consider hybrid algorithms for finding common elements of the set of common fixed points of two families quasi-C-non-expansive mappings and the set of solutions of an equilibrium problem. We establish strong convergence theorems of common elements in uniformly smooth and strictly convex Banach spaces with the property (K).
基金Supported by the National Natural Science Foundation of China (Grant No. 10771050)
文摘The purpose of this article is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-φ-asymptotically nonexpansive mappings.Its results hold in reflexive,strictly convex,smooth Banach spaces with the property(K).The results of this paper improve and extend recent some relative results.
基金supported by the National Natural Science Foundations of China under grant numbers Nos.11571206,91130003 and 11171189.
文摘In this paper,we investigate the mean-square convergence of the split-step q-scheme for nonlinear stochastic differential equations with jumps.Under some standard assumptions,we rigorously prove that the strong rate of convergence of the splitstep q-scheme in strong sense is one half.Some numerical experiments are carried out to assert our theoretical result.
基金supported by Korea Research Foundation Grant(KRF-2001-005-D00002)
文摘A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991).
基金supported by the Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems and Basic Scientific Research in Colleges and Universities of Heilongjiang Province(SFP of Heilongjiang University,No.KJCX201924).
文摘In this paper,we consider the Euler-Maruyama method for a class of stochastic Volterra integral equations(SVIEs).It is known that the strong convergence order of the EulerMaruyama method is 12.However,the strong superconvergence order 1 can be obtained for a class of SVIEs if the kernelsσi(t,t)=0 for i=1 and 2;otherwise,the strong convergence order is 12.Moreover,the theoretical results are illustrated by some numerical examples.
基金Supported by Beijing Municipal Natural Science Foundation(1192013).
文摘We consider a nonlinear stochastic Volterra integral equation with time-dependent delay and the corresponding Euler-Maruyama method in this paper.Strong convergence rate(at fixed point)of the corresponding Euler-Maruyama method is obtained when coefficients f and g both satisfy local Lipschitz and linear growth conditions.An example is provided to interpret our conclusions.Our result generalizes and improves the conclusion in[J.Gao,H.Liang,S.Ma,Strong convergence of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations with constant delay,Appl.Math.Comput.,348(2019)385-398.]
基金work of the first author was partially supported by the NSF grant DMS-1318486The work of the second author was partially supported by the startup grant from University of Central Florida.
文摘This paper develops and analyzes a fully discrete finite element method for a class of semilinear stochastic partial differential equations(SPDEs)with multiplicative noise.The nonlinearity in the diffusion term of the SPDEs is assumed to be globally Lipschitz and the nonlinearity in the drift term is only assumed to satisfy a one-sided Lipschitz condition.These assumptions are the same ones as the cases where numerical methods for general nonlinear stochastic ordinary differential equations(SODEs)under“minimum assumptions”were studied.As a result,the semilinear SPDEs considered in this paper are a direct generalization of these nonlinear SODEs.There are several difficulties which need to be overcome for this generalization.First,obviously the spatial discretization,which does not appear in the SODE case,adds an extra layer of difficulty.It turns out a spatial discretization must be designed to guarantee certain properties for the numerical scheme and its stiffness matrix.In this paper we use a finite element interpolation technique to discretize the nonlinear drift term.Second,in order to prove the strong convergence of the proposed fully discrete finite element method,stability estimates for higher order moments of the H1-seminorm of the numerical solution must be established,which are difficult and delicate.A judicious combination of the properties of the drift and diffusion terms and some nontrivial techniques is used in this paper to achieve the goal.Finally,stability estimates for the second and higher order moments of the L^(2)-norm of the numerical solution are also difficult to obtain due to the fact that the mass matrix may not be diagonally dominant.This is done by utilizing the interpolation theory and the higher moment estimates for the H1-seminorm of the numerical solution.After overcoming these difficulties,it is proved that the proposed fully discrete finite element method is convergent in strong norms with nearly optimal rates of convergence.Numerical experiment results are also presented to validate the theoretical results and to demonstrate the efficiency of the proposed numerical method.
基金The research of D.Liu and C.Huang is supported by National Science Foundation DMS0845061.
文摘In this paper,we revisit the Nested Stochastic Simulation Algorithm(NSSA)for stochastic chemical reacting networks by first proving its strong convergence.We then study a speed up of the algorithm by using the explicit Tau-Leaping method as the Inner solver to approximate invariant measures of fast processes,for which strong error estimates can also be obtained.Numerical experiments are presented to demonstrate the validity of our analysis.
基金supported by the Science and Technology Project of Education Department of Fujian Province(Grant number:JA13363)
文摘The purpose of this paper is to introduce a split generalized mixed equi- librium problem (SGMEP) and consider some iterative sequences to find a solution of the generalized mixed equilibrium problem such that its image un- der a given bounded linear operator is a solution of another generalized mixed equilibrium problem. We obtain some weak and strong convergence theorems.
文摘In this paper, strong summability of Cesaro means (of critical order) of Fourier-Laplace series on unit sphere is discussed. The Pointwise convergence conditions are established. The results of this paper are anal-ogous to those of single and multiple Fourier series.