The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generali...The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .展开更多
In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x...In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.展开更多
Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a m...Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator.Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature.In this paper,we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity.We propose two weakly convergent iterative algorithms and one strongly convergent algorithm.We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction.Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.展开更多
In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-stro...In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces. Then we study the weak convergence of the two iterative sequences. Our results improve and extend the results announced by many others.展开更多
In this paper,we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit.As an application,we obtain the convergence of random attractors ...In this paper,we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit.As an application,we obtain the convergence of random attractors for non-autonomous stochastic reactiondiffusion equations on unbounded domains,when the density of stochastic noises approaches zero.The weak convergence of solutions is proved by means of Alaoglu weak compactness theorem.A differentiability condition on nonlinearity is omitted,which implies that the existence conditions for random attractors are sufficient to ensure their upper semi-continuity.These results greatly strengthen the upper semi-continuity notion that has been developed in the literature.展开更多
The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.
In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes {Bn（s, t）}n∈N defined by Bn（s,t）=...In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes {Bn（s, t）}n∈N defined by Bn（s,t）=∫0^s∫0^tKa（s）（s,u）Kβ（t）（t,v）θn（u,u）dudu,where {θn（u, v））,n∈N is a family of processes, converging in law to a Brownian sheet as n -＊ oo, based on the well known Donsker＇s theorem.展开更多
A special approximation to Rosenblatt process with the finite-time interval representation was obtained. The construction of approximation family was based on the Poisson process. The proof to the approximation was di...A special approximation to Rosenblatt process with the finite-time interval representation was obtained. The construction of approximation family was based on the Poisson process. The proof to the approximation was divided into two aspects. Firstly, the approximation family was tight using the methods given by Billingsley; secondly, the finite-dimension distributions of approximation family converged weakly to the Rosenblatt process by proving the convergence of the corresponding characteristic functions.展开更多
This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise.The existence of invariant measures is establis...This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise.The existence of invariant measures is established using the classical Krylov-Bogoliubov theory.The uniqueness of invariant measures and the weak convergence of transition probabilities are demonstrated through the application of the asymptotic coupling method and Foias-Prodi estimate.展开更多
In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the c...In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].展开更多
A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes.The process can also be obtained by the pathwise unique solution to a stochastic equati...A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes.The process can also be obtained by the pathwise unique solution to a stochastic equation system.From the stochastic equation system we derive the distribution of local jumps and give the exponential ergodicity in Wasserstein-type distances of the transition semigroup.Meanwhile,we study immigration structures associated with the process and prove the existence of the stationary distribution of the process with immigration.展开更多
In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend t...In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.展开更多
In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a s...In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a static solid wall and a free boundary connected to a vacuum state. We take the homogeneous boundary conditions for velocity, microrotation and heat flux on the solid border and that the normal stress, heat flux and microrotation are equal to zero on the free boundary. The proof of the global existence of the solution is based on a limit procedure. We define the finite difference approximate equations system and construct the sequence of approximate solutions that converges to the solution of our problem globally in time.展开更多
Evolutionary computation is a kind of adaptive non--numerical computation method which is designed tosimulate evolution of nature. In this paper, evolutionary algorithm behavior is described in terms of theconstructio...Evolutionary computation is a kind of adaptive non--numerical computation method which is designed tosimulate evolution of nature. In this paper, evolutionary algorithm behavior is described in terms of theconstruction and evolution of the sampling distributions over the space of candidate solutions. Iterativeconstruction of the sampling distributions is based on the idea of the global random search of generationalmethods. Under this frame, propontional selection is characterized as a gobal search operator, and recombination is characerized as the search process that exploits similarities. It is shown-that by properly constraining the search breadth of recombination operators, weak convergence of evolutionary algorithms to aglobal optimum can be ensured.展开更多
We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
In this paper, A nonparametric hazard estimator is introduced. Weak convergence and strong uniformly consistency of the proposed estimator lambda(n)(t) are investigated on a bounded interval, respectively. An asymptot...In this paper, A nonparametric hazard estimator is introduced. Weak convergence and strong uniformly consistency of the proposed estimator lambda(n)(t) are investigated on a bounded interval, respectively. An asymptotic representation of lambda(n)(t) is also given, and the asymptotic representation is used to prove asymptotic normality of the hazard estimator.展开更多
This paper studies the limit distributions for discretization error of irregular sam- pling approximations of stochastic integral. The irregular sampling approximation was first presented in Hayashi et al.[3], which w...This paper studies the limit distributions for discretization error of irregular sam- pling approximations of stochastic integral. The irregular sampling approximation was first presented in Hayashi et al.[3], which was more general than the sampling approximation in Lindberg and Rootzen [10]. As applications, we derive the asymptotic distribution of hedging error and the Euler scheme of stochastic differential equation respectively.展开更多
In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization prob...In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization problems. We then prove convergence theorems under mild conditions. Finally, we provide numerical experiments on image restoration problem and image inpainting problem. The numerical results show that the proposed algorithms have more efficient than known algorithms introduced in the literature.展开更多
In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hy...In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hysteresis differential operator are given.展开更多
This paper considers diffusion processes {X^(?)(t)} on R^2, which are perturbations of dynamical system {X(t)} (dX(t)=b(X(t))dt) on R^2. By means of weak convergence of probability measures, the authors characterize t...This paper considers diffusion processes {X^(?)(t)} on R^2, which are perturbations of dynamical system {X(t)} (dX(t)=b(X(t))dt) on R^2. By means of weak convergence of probability measures, the authors characterize the limit behavior for empirical measures of {X^(?)(t)} in a neighborhood domain of saddle point of the dynamical system as the perturbations tend to zero.展开更多
文摘The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .
基金Partially supported by NSFC(No.11701304)the K.C.Wong Education Foundation。
文摘In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.
文摘Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator.Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature.In this paper,we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity.We propose two weakly convergent iterative algorithms and one strongly convergent algorithm.We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction.Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.
文摘In this paper, we introduce two new iterative algorithms for finding a common element of the set of solutions of a general equilibrium problem and the set of solutions of the variational inequality for an inverse-strongly monotone operator and the set of common fixed points of two infinite families of relatively nonexpansive mappings or the set of common fixed points of an infinite family of relatively quasi-nonexpansive mappings in Banach spaces. Then we study the weak convergence of the two iterative sequences. Our results improve and extend the results announced by many others.
文摘In this paper,we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit.As an application,we obtain the convergence of random attractors for non-autonomous stochastic reactiondiffusion equations on unbounded domains,when the density of stochastic noises approaches zero.The weak convergence of solutions is proved by means of Alaoglu weak compactness theorem.A differentiability condition on nonlinearity is omitted,which implies that the existence conditions for random attractors are sufficient to ensure their upper semi-continuity.These results greatly strengthen the upper semi-continuity notion that has been developed in the literature.
文摘The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.
基金partially supported by National Natural Science Foundation of China(Grant Nos.1140131311771209)+6 种基金partially supported by National Natural Science Foundation of China(Grant No.11426036)Natural Science Foundation of Jiangsu Province(Grant No.BK20161579)China Postdoctoral Science Foundation(Grant Nos.2014M5603682015T80475)2014 Qing Lan ProjectNatural Science Foundation of Anhui Province(Grant No.1408085QA10)Key Natural Science Foundation of Anhui Education Commission(Grant No.KJ2016A453)
文摘In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes {Bn（s, t）}n∈N defined by Bn（s,t）=∫0^s∫0^tKa（s）（s,u）Kβ（t）（t,v）θn（u,u）dudu,where {θn（u, v））,n∈N is a family of processes, converging in law to a Brownian sheet as n -＊ oo, based on the well known Donsker＇s theorem.
基金National Natural Science Foundation of China(No. 11171062)Innovation Program of Shanghai Municipal Education Commission,China(No. 12ZZ063)Natural Science Foundation of Bengbu College,China(No. 2010ZR10)
文摘A special approximation to Rosenblatt process with the finite-time interval representation was obtained. The construction of approximation family was based on the Poisson process. The proof to the approximation was divided into two aspects. Firstly, the approximation family was tight using the methods given by Billingsley; secondly, the finite-dimension distributions of approximation family converged weakly to the Rosenblatt process by proving the convergence of the corresponding characteristic functions.
基金supported in part by the NSFC(12171084,12326367)the Jiangsu Provincial Scientific Research Center of Applied Mathematics(BK20233002)the fundamental Research Funds for the Central Universities(RF1028623037)。
文摘This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise.The existence of invariant measures is established using the classical Krylov-Bogoliubov theory.The uniqueness of invariant measures and the weak convergence of transition probabilities are demonstrated through the application of the asymptotic coupling method and Foias-Prodi estimate.
文摘In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].
基金supported by the National Key R&D Program of China(2020YFA0712900)the National Natural Science Foundation of China(11531001).
文摘A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes.The process can also be obtained by the pathwise unique solution to a stochastic equation system.From the stochastic equation system we derive the distribution of local jumps and give the exponential ergodicity in Wasserstein-type distances of the transition semigroup.Meanwhile,we study immigration structures associated with the process and prove the existence of the stationary distribution of the process with immigration.
基金supported by National Natural Science Foundation of China (10901054)
文摘In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.
基金supported by Scientific Research of the University of Rijeka(13.14.1.3.03)
文摘In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a static solid wall and a free boundary connected to a vacuum state. We take the homogeneous boundary conditions for velocity, microrotation and heat flux on the solid border and that the normal stress, heat flux and microrotation are equal to zero on the free boundary. The proof of the global existence of the solution is based on a limit procedure. We define the finite difference approximate equations system and construct the sequence of approximate solutions that converges to the solution of our problem globally in time.
文摘Evolutionary computation is a kind of adaptive non--numerical computation method which is designed tosimulate evolution of nature. In this paper, evolutionary algorithm behavior is described in terms of theconstruction and evolution of the sampling distributions over the space of candidate solutions. Iterativeconstruction of the sampling distributions is based on the idea of the global random search of generationalmethods. Under this frame, propontional selection is characterized as a gobal search operator, and recombination is characerized as the search process that exploits similarities. It is shown-that by properly constraining the search breadth of recombination operators, weak convergence of evolutionary algorithms to aglobal optimum can be ensured.
文摘We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
文摘In this paper, A nonparametric hazard estimator is introduced. Weak convergence and strong uniformly consistency of the proposed estimator lambda(n)(t) are investigated on a bounded interval, respectively. An asymptotic representation of lambda(n)(t) is also given, and the asymptotic representation is used to prove asymptotic normality of the hazard estimator.
基金Supported by the National Natural Science Foundation of China(11371317)
文摘This paper studies the limit distributions for discretization error of irregular sam- pling approximations of stochastic integral. The irregular sampling approximation was first presented in Hayashi et al.[3], which was more general than the sampling approximation in Lindberg and Rootzen [10]. As applications, we derive the asymptotic distribution of hedging error and the Euler scheme of stochastic differential equation respectively.
基金supported by National Research Council of Thailand (NRCT) under grant no. N41A640094the Thailand Science Research and Innovation Fund and the University of Phayao under the project FF66-UoE。
文摘In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization problems. We then prove convergence theorems under mild conditions. Finally, we provide numerical experiments on image restoration problem and image inpainting problem. The numerical results show that the proposed algorithms have more efficient than known algorithms introduced in the literature.
基金the Natural Science Foundation of the Education Committee of Anhui Provinc
文摘In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hysteresis differential operator are given.
基金Partially supported by the National Natural Science Foundation of China
文摘This paper considers diffusion processes {X^(?)(t)} on R^2, which are perturbations of dynamical system {X(t)} (dX(t)=b(X(t))dt) on R^2. By means of weak convergence of probability measures, the authors characterize the limit behavior for empirical measures of {X^(?)(t)} in a neighborhood domain of saddle point of the dynamical system as the perturbations tend to zero.
