Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augme...Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Two conditions guaranteeing such convergence include exponential ergodicity and stochastic monotonicity of the process. The same also holds for processes dominated by a stochastically monotone Markov process. In addition, we shall show that finite perturbations of stochastically monotone processes may be viewed as being dominated by a stochastically monotone process, thus extending the scope of these results to a larger class of processes. Consequently, the augmentation method provides an attractive, intuitive method for approximating the stationary distributions of a large class of Markov processes on countably infinite state spaces from a finite amount of known information.展开更多
Let X be a space of homogenous type and ψ： X × [0,∞） → [0,∞） be a growth function such that ψ（·,t） is a Muckenhoupt weight uniformly in t and ψ（x,·） an Orlicz function of uniformly upper ty...Let X be a space of homogenous type and ψ： X × [0,∞） → [0,∞） be a growth function such that ψ（·,t） is a Muckenhoupt weight uniformly in t and ψ（x,·） an Orlicz function of uniformly upper type 1 and lower type p ∈（0,1].In this article,the authors introduce a new Musielak–Orlicz BMO-type space BMOψA（X） associated with the generalized approximation to the identity,give out its basic properties and establish its two equivalent characterizations,respectively,in terms of the spaces BMOψA,max（X） and BMOψA（X）.Moreover,two variants of the John–Nirenberg inequality on BMOψA（X） are obtained.As an application,the authors further prove that the space BMOψΔ1/2（Rn）,associated with the Poisson semigroup of the Laplace operator Δ on Rn,coincides with the space BMOψ（Rn） introduced by Ky.展开更多
In this paper, we firstly define a decreasing sequence {Pn(S)} by the generation of the Sierpinski gasket where each Pn(S) can be obtained in finite steps. Then we prove that the Hausdorff measure Hs(S) of the Sierpin...In this paper, we firstly define a decreasing sequence {Pn(S)} by the generation of the Sierpinski gasket where each Pn(S) can be obtained in finite steps. Then we prove that the Hausdorff measure Hs(S) of the Sierpinski gasket S can be approximated by {Pn(S)} with Pn(S)/(l + l/2n-3)s≤Hs(S)≤ Pn(S). An algorithm is presented to get Pn(S) for n ≤5. As an application, we obtain the best lower bound of Hs(S) till now: Hs(S)≥0.5631.展开更多
随着工业生产中数据源的不断增加,人们对数据流的处理需求日益增大.其中,一个基本需求是基于距离度量方法的子序列匹配.由于动态时间弯曲距离(dynamic time warping,DTW)具有较高的度量精度,将其应用于子序列匹配问题是非常有价值的.但...随着工业生产中数据源的不断增加,人们对数据流的处理需求日益增大.其中,一个基本需求是基于距离度量方法的子序列匹配.由于动态时间弯曲距离(dynamic time warping,DTW)具有较高的度量精度,将其应用于子序列匹配问题是非常有价值的.但是,DTW具有较高的计算复杂度,这极大地限制了它在数据流上的应用.针对该问题,设计了一种高效的基于DTW的数据流子序列匹配系统.首先对数据流进行高效的适应性分段,然后对每一子段进行切比雪夫因式分解.不同于在原始数据空间的DTW计算,系统将在低维的切比雪夫特征空间计算DTW距离,因此,系统具有较高的计算效率.另外,提出了一种高效的在线匹配算法,可实现DTW在数据流上的增量式计算,进一步提高了系统的执行效率.展开更多
This paper is to decide the nuclear operator on the space of vector valued continuous functions through the representing measure by considering a Radon Nikodym property of the space of nu...This paper is to decide the nuclear operator on the space of vector valued continuous functions through the representing measure by considering a Radon Nikodym property of the space of nuclear operators.展开更多
This article is concerned with the weak convergence of invariant measures asso- ciated with multivalued stochastic differential equations in the finite dimensional space.
Recently, some scholars such as Boccardo, Callout and Rakotoson, studied studied the second-order partial differential equation u=f, where f∈L^1(Ω) (non-reflexive), more generally f∈M(Ω), M(Ω)=[C_c(Ω)]＇, the to...Recently, some scholars such as Boccardo, Callout and Rakotoson, studied studied the second-order partial differential equation u=f, where f∈L^1(Ω) (non-reflexive), more generally f∈M(Ω), M(Ω)=[C_c(Ω)]＇, the topological dual of C_c(Ω), is also called the set of Radon-measures. A classical example is f=δ(the measure of Dirac), δ∈M(Ω). In brief, they proved the existence of weak solution for a quasilinear elliptic problem: -div((x, u, Du))=f∈M(Ω), u|_αΩ=0, in which ΩR^N, is展开更多
Let G be an open subset in the extended complex plane and let A（G） denote the algebra of all functions analytic on G and continuous on G. We call a domain multi-nicely connected if there is a circular domain W and a...Let G be an open subset in the extended complex plane and let A（G） denote the algebra of all functions analytic on G and continuous on G. We call a domain multi-nicely connected if there is a circular domain W and a conformal map ~ from W onto G such that the boundary value function of φ is univalent almost everywhere with respect to the arclength on aW. Suppose that every component of G is finitely connected and none of the components of G have single point boundary components. We show that for every bounded analytic function on G to be the pointwise limit of a bounded sequence of functions in A（G）, it is necessary and sufficient that each component of G is multi-nicely connected and the harmonic measures of G are mutually singular. This generalizes the corresponding result of Davie for the case when the components of G are simply connected.展开更多
A new concept of convergence （R-convergence） of a sequence of measures is applied to characterize global minimizers in a functional space as a sequence of approximate solutions in finite-dimensional spaces. A deviat...A new concept of convergence （R-convergence） of a sequence of measures is applied to characterize global minimizers in a functional space as a sequence of approximate solutions in finite-dimensional spaces. A deviation integral approach is used to find such solutions. For a constrained problem, a penalized deviation integral algorithm is proposed to convert it to unconstrained ones. A numerical example on an optimal control problem with non-convex state constraints is given to show the effectiveness of the algorithm.展开更多
文摘Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Two conditions guaranteeing such convergence include exponential ergodicity and stochastic monotonicity of the process. The same also holds for processes dominated by a stochastically monotone Markov process. In addition, we shall show that finite perturbations of stochastically monotone processes may be viewed as being dominated by a stochastically monotone process, thus extending the scope of these results to a larger class of processes. Consequently, the augmentation method provides an attractive, intuitive method for approximating the stationary distributions of a large class of Markov processes on countably infinite state spaces from a finite amount of known information.
基金supported by National Natural Science Foundation of China(Grant Nos.11171027 and 11361020)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120003110003)the Fundamental Research Funds for Central Universities of China(Grant Nos.2012LYB26,2012CXQT09 and lzujbky-2014-18)
文摘Let X be a space of homogenous type and ψ： X × [0,∞） → [0,∞） be a growth function such that ψ（·,t） is a Muckenhoupt weight uniformly in t and ψ（x,·） an Orlicz function of uniformly upper type 1 and lower type p ∈（0,1].In this article,the authors introduce a new Musielak–Orlicz BMO-type space BMOψA（X） associated with the generalized approximation to the identity,give out its basic properties and establish its two equivalent characterizations,respectively,in terms of the spaces BMOψA,max（X） and BMOψA（X）.Moreover,two variants of the John–Nirenberg inequality on BMOψA（X） are obtained.As an application,the authors further prove that the space BMOψΔ1/2（Rn）,associated with the Poisson semigroup of the Laplace operator Δ on Rn,coincides with the space BMOψ（Rn） introduced by Ky.
文摘In this paper, we firstly define a decreasing sequence {Pn(S)} by the generation of the Sierpinski gasket where each Pn(S) can be obtained in finite steps. Then we prove that the Hausdorff measure Hs(S) of the Sierpinski gasket S can be approximated by {Pn(S)} with Pn(S)/(l + l/2n-3)s≤Hs(S)≤ Pn(S). An algorithm is presented to get Pn(S) for n ≤5. As an application, we obtain the best lower bound of Hs(S) till now: Hs(S)≥0.5631.
文摘随着工业生产中数据源的不断增加,人们对数据流的处理需求日益增大.其中,一个基本需求是基于距离度量方法的子序列匹配.由于动态时间弯曲距离(dynamic time warping,DTW)具有较高的度量精度,将其应用于子序列匹配问题是非常有价值的.但是,DTW具有较高的计算复杂度,这极大地限制了它在数据流上的应用.针对该问题,设计了一种高效的基于DTW的数据流子序列匹配系统.首先对数据流进行高效的适应性分段,然后对每一子段进行切比雪夫因式分解.不同于在原始数据空间的DTW计算,系统将在低维的切比雪夫特征空间计算DTW距离,因此,系统具有较高的计算效率.另外,提出了一种高效的在线匹配算法,可实现DTW在数据流上的增量式计算,进一步提高了系统的执行效率.
文摘This paper is to decide the nuclear operator on the space of vector valued continuous functions through the representing measure by considering a Radon Nikodym property of the space of nuclear operators.
基金supported by NSFs of China(11471340 and 11461028)
文摘This article is concerned with the weak convergence of invariant measures asso- ciated with multivalued stochastic differential equations in the finite dimensional space.
文摘Recently, some scholars such as Boccardo, Callout and Rakotoson, studied studied the second-order partial differential equation u=f, where f∈L^1(Ω) (non-reflexive), more generally f∈M(Ω), M(Ω)=[C_c(Ω)]＇, the topological dual of C_c(Ω), is also called the set of Radon-measures. A classical example is f=δ(the measure of Dirac), δ∈M(Ω). In brief, they proved the existence of weak solution for a quasilinear elliptic problem: -div((x, u, Du))=f∈M(Ω), u|_αΩ=0, in which ΩR^N, is
文摘Let G be an open subset in the extended complex plane and let A（G） denote the algebra of all functions analytic on G and continuous on G. We call a domain multi-nicely connected if there is a circular domain W and a conformal map ~ from W onto G such that the boundary value function of φ is univalent almost everywhere with respect to the arclength on aW. Suppose that every component of G is finitely connected and none of the components of G have single point boundary components. We show that for every bounded analytic function on G to be the pointwise limit of a bounded sequence of functions in A（G）, it is necessary and sufficient that each component of G is multi-nicely connected and the harmonic measures of G are mutually singular. This generalizes the corresponding result of Davie for the case when the components of G are simply connected.
基金Project supported by the National Natural Science Foundation of China(No.11071158)Shanghai Leading Academic Discipline Project(No.S30104)
文摘A new concept of convergence （R-convergence） of a sequence of measures is applied to characterize global minimizers in a functional space as a sequence of approximate solutions in finite-dimensional spaces. A deviation integral approach is used to find such solutions. For a constrained problem, a penalized deviation integral algorithm is proposed to convert it to unconstrained ones. A numerical example on an optimal control problem with non-convex state constraints is given to show the effectiveness of the algorithm.
