In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order ...In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.展开更多
As a popular distributed machine learning framework,wireless federated edge learning(FEEL)can keep original data local,while uploading model training updates to protect privacy and prevent data silos.However,since wir...As a popular distributed machine learning framework,wireless federated edge learning(FEEL)can keep original data local,while uploading model training updates to protect privacy and prevent data silos.However,since wireless channels are usually unreliable,there is no guarantee that the model updates uploaded by local devices are correct,thus greatly degrading the performance of the wireless FEEL.Conventional retransmission schemes designed for wireless systems generally aim to maximize the system throughput or minimize the packet error rate,which is not suitable for the FEEL system.A novel retransmission scheme is proposed for the FEEL system to make a tradeoff between model training accuracy and retransmission latency.In the proposed scheme,a retransmission device selection criterion is first designed based on the channel condition,the number of local data,and the importance of model updates.In addition,we design the air interface signaling under this retransmission scheme to facilitate the implementation of the proposed scheme in practical scenarios.Finally,the effectiveness of the proposed retransmission scheme is validated through simulation experiments.展开更多
In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of nor...In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).展开更多
Let B^(H) be a fractional Brownian motion with Hurst index 1/2≤H<1.In this paper,we consider the equation(called the Ornstein-Uhlenbeck process with a linear self-repelling drift)dX_(t)^(H)=dB_(t)^(H)+σ X_(t)^(H)...Let B^(H) be a fractional Brownian motion with Hurst index 1/2≤H<1.In this paper,we consider the equation(called the Ornstein-Uhlenbeck process with a linear self-repelling drift)dX_(t)^(H)=dB_(t)^(H)+σ X_(t)^(H)dt+vdt-θ(∫_(0)^(t)(X_(t)^(H)-X_(s)^(H))ds)dt,whereθ<0,σ,v∈ℝ.The process is an analogue of self-attracting diffusion(Cranston,Le Jan.Math Ann,1995,303:87–93).Our main aim is to study the large time behaviors of the process.We show that the solution X^(H)diverges to infinity as t tends to infinity,and obtain the speed at which the process X^(H)diverges to infinity.展开更多
In this paper, we combine the method of constructing the compensating function introduced by Kawashima and the standard energy method for the study on the Landau equation with external forcing. Both the global existen...In this paper, we combine the method of constructing the compensating function introduced by Kawashima and the standard energy method for the study on the Landau equation with external forcing. Both the global existence of solutions near the time asymptotic states which are local Maxwellians and the optimal convergence rates are obtained. The method used here has its own advantage for this kind of studies because it does not involve the spectrum analysis of the corresponding linearized operator.展开更多
This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation techn...This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ...展开更多
This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fac...This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fact that the initial disturbance can be chosen large in suitable norm. Our analysis is based on the L^1-stability results obtained by C. Mascia and R. Natalini in [12].展开更多
In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp (f) of fractional Brownian motion of Hurst parameter H 〈 1/2 when the fractional Brownian motion i...In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp (f) of fractional Brownian motion of Hurst parameter H 〈 1/2 when the fractional Brownian motion is replaced by its polygonal approximation. Under different conditions on f and for different p, we obtain different rates.展开更多
We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in ...We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.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 this paper, we consider a class of reaction hyperbolic systems for axonal trans- port arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hy...In this paper, we consider a class of reaction hyperbolic systems for axonal trans- port arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hyperbolic systems converge toward to the unique entropy solution of the equilibrium equation at the optimal rate O(√δ) in L1 norm as the relaxation time δ tends to zero.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 paper, we have investigated the problem of the convergence rate of the multiple integralwhere f ∈ Cn+1([0, T ]n) is a given function, π is a partition of the interval [0, T ] and {BtHi ,π} is a family of...In this paper, we have investigated the problem of the convergence rate of the multiple integralwhere f ∈ Cn+1([0, T ]n) is a given function, π is a partition of the interval [0, T ] and {BtHi ,π} is a family of interpolation approximation of fractional Brownian motion BtH with Hurst parameter H 1/2. The limit process is the multiple Stratonovich integral of the function f . In view of known results, the convergence rate is different for different multiplicity n. Under some mild conditions, we obtain that the uniform convergence rate is 2H in the mean square sense, where is the norm of the partition generating the approximations.展开更多
For the viscous and heat-conductive fluids governed by the compressible Navier- Stokes equations with external force of general form in R^3, there exist nontrivial stationary solutions provided the external forces are...For the viscous and heat-conductive fluids governed by the compressible Navier- Stokes equations with external force of general form in R^3, there exist nontrivial stationary solutions provided the external forces are small in suitable norms, which was studied in article [15], and there we also proved the global in time stability of the stationary solutions with respect to initial data in H^3-framework. In this article, the authors investigate the rates of convergence of nonstationary solutions to the corresponding stationary solutions when the initial data are small in H^3 and bounded in L6/5.展开更多
New synchronization algorithm and analysis of its convergence rate for clock oscillators in dynamical network with time-delays are presented.A network of nodes equipped with hardware clock oscillators with bounded dri...New synchronization algorithm and analysis of its convergence rate for clock oscillators in dynamical network with time-delays are presented.A network of nodes equipped with hardware clock oscillators with bounded drift is considered.Firstly,a dynamic synchronization algorithm based on consensus control strategy,namely fast averaging synchronization algorithm (FASA),is presented to find the solutions to the synchronization problem.By FASA,each node computes the logical clock value based on its value of hardware clock and message exchange.The goal is to synchronize all the nodes' logical clocks as closely as possible.Secondly,the convergence rate of FASA is analyzed that proves it is related to the bound by a nondecreasing function of the uncertainty in message delay and network parameters.Then,FASA's convergence rate is proven by means of the robust optimal design.Meanwhile,several practical applications for FASA,especially the application to inverse global positioning system (IGPS) base station network are discussed.Finally,numerical simulation results demonstrate the correctness and efficiency of the proposed FASA.Compared FASA with traditional clock synchronization algorithms (CSAs),the convergence rate of the proposed algorithm converges faster than that of the CSAs evidently.展开更多
Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on del...Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on delay differential inequality. The method, which does not make use of any Lyapunov functional, is simple and valid for the stability analysis of neural networks with delay. Some previously established results in this paper are shown to be special casses of the presented result.展开更多
In this paper,we introduce the Bézier variant of two new families of generalized Bernstein type operators.We establish a direct approximation by means of the Ditzian-Totik modulus of smoothness and a global appro...In this paper,we introduce the Bézier variant of two new families of generalized Bernstein type operators.We establish a direct approximation by means of the Ditzian-Totik modulus of smoothness and a global approximation theorem in terms of second order modulus of continuity.By means of construction of suitable functions and the method of Bojanic and Cheng,we give the rate of convergence for absolutely continuous functions having a derivative equivalent to a bounded variation function.展开更多
For bounded or some locally bounded functions f measurable on an interval I there is estimated the rate of convergence of the Durrmeyer-type operators Lnf at those points x∈IntI at which the one-sided limits f(x±...For bounded or some locally bounded functions f measurable on an interval I there is estimated the rate of convergence of the Durrmeyer-type operators Lnf at those points x∈IntI at which the one-sided limits f(x± 0) exist. In the main theorems the Chanturiya's modulus of variation is used.展开更多
This paper discusses the convergence rates about a class of evolutionary algorithms in general search spaces by means of the ergodic theory in Markov chain and some techniques in Banach algebra. Under certain conditio...This paper discusses the convergence rates about a class of evolutionary algorithms in general search spaces by means of the ergodic theory in Markov chain and some techniques in Banach algebra. Under certain conditions that transition probability functions of Markov chains corresponding to evolutionary algorithms satisfy, the authors obtain the convergence rates of the exponential order. Furthermore, they also analyze the characteristics of the conditions which can be met by genetic operators and selection strategies.展开更多
The Cauchy problem of the Landau equation with frictional force is investigated. Based on Fourier analysis and nonlinear energy estimates, the optimal convergence rate to the steady state is obtained under some condit...The Cauchy problem of the Landau equation with frictional force is investigated. Based on Fourier analysis and nonlinear energy estimates, the optimal convergence rate to the steady state is obtained under some conditions on initial data.展开更多
文摘In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.
文摘As a popular distributed machine learning framework,wireless federated edge learning(FEEL)can keep original data local,while uploading model training updates to protect privacy and prevent data silos.However,since wireless channels are usually unreliable,there is no guarantee that the model updates uploaded by local devices are correct,thus greatly degrading the performance of the wireless FEEL.Conventional retransmission schemes designed for wireless systems generally aim to maximize the system throughput or minimize the packet error rate,which is not suitable for the FEEL system.A novel retransmission scheme is proposed for the FEEL system to make a tradeoff between model training accuracy and retransmission latency.In the proposed scheme,a retransmission device selection criterion is first designed based on the channel condition,the number of local data,and the importance of model updates.In addition,we design the air interface signaling under this retransmission scheme to facilitate the implementation of the proposed scheme in practical scenarios.Finally,the effectiveness of the proposed retransmission scheme is validated through simulation experiments.
文摘In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).
文摘Let B^(H) be a fractional Brownian motion with Hurst index 1/2≤H<1.In this paper,we consider the equation(called the Ornstein-Uhlenbeck process with a linear self-repelling drift)dX_(t)^(H)=dB_(t)^(H)+σ X_(t)^(H)dt+vdt-θ(∫_(0)^(t)(X_(t)^(H)-X_(s)^(H))ds)dt,whereθ<0,σ,v∈ℝ.The process is an analogue of self-attracting diffusion(Cranston,Le Jan.Math Ann,1995,303:87–93).Our main aim is to study the large time behaviors of the process.We show that the solution X^(H)diverges to infinity as t tends to infinity,and obtain the speed at which the process X^(H)diverges to infinity.
基金supported by Strategic Research Grant of City University of Hong Kong, 7002129the Changjiang Scholar Program of Chinese Educational Ministry in Shanghai Jiao Tong University+1 种基金The research of the second author was supported partially by NSFC (10601018)partially by FANEDD
文摘In this paper, we combine the method of constructing the compensating function introduced by Kawashima and the standard energy method for the study on the Landau equation with external forcing. Both the global existence of solutions near the time asymptotic states which are local Maxwellians and the optimal convergence rates are obtained. The method used here has its own advantage for this kind of studies because it does not involve the spectrum analysis of the corresponding linearized operator.
基金supported by the NSF China#10571075NSF-Guangdong China#04010473+1 种基金The research of the second author was supported by Jinan University Foundation#51204033the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State education Ministry#2005-383
文摘This article is concerned with the pointwise error estimates for vanishing vis- cosity approximations to scalar convex conservation laws with boundary.By the weighted error function and a bootstrap extrapolation technique introduced by Tadmor-Tang,an optimal pointwise convergence rate is derived for the vanishing viscosity approximations to the initial-boundary value problem for scalar convex conservation laws,whose weak entropy solution is piecewise C 2 -smooth with interaction of elementary waves and the ...
基金The subject is supported by National Natural Sciences Foundation of China(10001036)
文摘This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fact that the initial disturbance can be chosen large in suitable norm. Our analysis is based on the L^1-stability results obtained by C. Mascia and R. Natalini in [12].
基金partially supported by NNSF of China (60534080)the firstauthor is supported in part by the National Science Foundation (DMS0504783)
文摘In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp (f) of fractional Brownian motion of Hurst parameter H 〈 1/2 when the fractional Brownian motion is replaced by its polygonal approximation. Under different conditions on f and for different p, we obtain different rates.
基金supported by the National Natural Science Foundation of China(11571052,11731012)the Hunan Provincial Natural Science Foundation of China(2018JJ2417)the Open Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering(2018MMAEZD02)。
文摘We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.
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partially supported by the NSFC(11371349)National Basic Research Program of China(973 Program)(2011CB808002)
文摘In this paper, we consider a class of reaction hyperbolic systems for axonal trans- port arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hyperbolic systems converge toward to the unique entropy solution of the equilibrium equation at the optimal rate O(√δ) in L1 norm as the relaxation time δ tends to zero.
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supported by the scientific research fund of Central South University for Nationalities (YZZ09005)
文摘In this paper, we have investigated the problem of the convergence rate of the multiple integralwhere f ∈ Cn+1([0, T ]n) is a given function, π is a partition of the interval [0, T ] and {BtHi ,π} is a family of interpolation approximation of fractional Brownian motion BtH with Hurst parameter H 1/2. The limit process is the multiple Stratonovich integral of the function f . In view of known results, the convergence rate is different for different multiplicity n. Under some mild conditions, we obtain that the uniform convergence rate is 2H in the mean square sense, where is the norm of the partition generating the approximations.
基金Sponsored by National Natural Science Foundation of China (10431060, 10329101)
文摘For the viscous and heat-conductive fluids governed by the compressible Navier- Stokes equations with external force of general form in R^3, there exist nontrivial stationary solutions provided the external forces are small in suitable norms, which was studied in article [15], and there we also proved the global in time stability of the stationary solutions with respect to initial data in H^3-framework. In this article, the authors investigate the rates of convergence of nonstationary solutions to the corresponding stationary solutions when the initial data are small in H^3 and bounded in L6/5.
基金Sponsored by the Cooperation Building Foundation Project of Beijing Education Committee (100070
文摘New synchronization algorithm and analysis of its convergence rate for clock oscillators in dynamical network with time-delays are presented.A network of nodes equipped with hardware clock oscillators with bounded drift is considered.Firstly,a dynamic synchronization algorithm based on consensus control strategy,namely fast averaging synchronization algorithm (FASA),is presented to find the solutions to the synchronization problem.By FASA,each node computes the logical clock value based on its value of hardware clock and message exchange.The goal is to synchronize all the nodes' logical clocks as closely as possible.Secondly,the convergence rate of FASA is analyzed that proves it is related to the bound by a nondecreasing function of the uncertainty in message delay and network parameters.Then,FASA's convergence rate is proven by means of the robust optimal design.Meanwhile,several practical applications for FASA,especially the application to inverse global positioning system (IGPS) base station network are discussed.Finally,numerical simulation results demonstrate the correctness and efficiency of the proposed FASA.Compared FASA with traditional clock synchronization algorithms (CSAs),the convergence rate of the proposed algorithm converges faster than that of the CSAs evidently.
文摘Some sufficient conditions for the global exponential stability and lower bounds on the rate of exponential convergence of the cellular neural networks with delay (DCNNs) are obtained by means of a method based on delay differential inequality. The method, which does not make use of any Lyapunov functional, is simple and valid for the stability analysis of neural networks with delay. Some previously established results in this paper are shown to be special casses of the presented result.
基金This work is supported by the National Natural Science Foundation of China(11601266)the Natural Science Foundation of Fujian Province of China(2016J05017)the Program for New Century Excellent Talents in Fujian Province University and the Program for Outstanding Youth Scientific Research Talents in Fujian Province University.
文摘In this paper,we introduce the Bézier variant of two new families of generalized Bernstein type operators.We establish a direct approximation by means of the Ditzian-Totik modulus of smoothness and a global approximation theorem in terms of second order modulus of continuity.By means of construction of suitable functions and the method of Bojanic and Cheng,we give the rate of convergence for absolutely continuous functions having a derivative equivalent to a bounded variation function.
文摘For bounded or some locally bounded functions f measurable on an interval I there is estimated the rate of convergence of the Durrmeyer-type operators Lnf at those points x∈IntI at which the one-sided limits f(x± 0) exist. In the main theorems the Chanturiya's modulus of variation is used.
基金This work is supported by the National Natural Science Foundation of ChinaVisiting Scholar Foundation of Key Lab, in Univers
文摘This paper discusses the convergence rates about a class of evolutionary algorithms in general search spaces by means of the ergodic theory in Markov chain and some techniques in Banach algebra. Under certain conditions that transition probability functions of Markov chains corresponding to evolutionary algorithms satisfy, the authors obtain the convergence rates of the exponential order. Furthermore, they also analyze the characteristics of the conditions which can be met by genetic operators and selection strategies.
基金the first author is supported by the National Natural Science Foundation of China (11101188)the second author is supported by the National Natural Science Foundation of China (10871082)supported by the Fundamental Research Funds for the Central Universities
文摘The Cauchy problem of the Landau equation with frictional force is investigated. Based on Fourier analysis and nonlinear energy estimates, the optimal convergence rate to the steady state is obtained under some conditions on initial data.