First,a class of strong limit theorems are proved by constructing two nonnegative martingales.Then they are applied to the study of all kinds of even-odd Markov chain fields and Markov chain fields defined in the pape...First,a class of strong limit theorems are proved by constructing two nonnegative martingales.Then they are applied to the study of all kinds of even-odd Markov chain fields and Markov chain fields defined in the paper.Finally,some strong limit theorems for the even-odd Markov chain fields and Markov chain fields are obtained.展开更多
This in virtue of the notion of likelihood ratio and the tool of moment generating function, the limit properties of the sequences of random discrete random variables are studied, and a class of strong deviation theor...This in virtue of the notion of likelihood ratio and the tool of moment generating function, the limit properties of the sequences of random discrete random variables are studied, and a class of strong deviation theorems which represented by inequalities between random variables and their expectation are obtained. As a result, we obtain some strong deviation theorems for Poisson distribution and binomial distribution.展开更多
In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class o...In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class of its equivalent forms.Based on this property,some strong limit theorems including conditional entropy density are studied for the tree-indexed Markov chains in random environment.展开更多
Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differen...Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differentials of unitary indeterminate forms. The fruit of this work is going to be reported in three parts. The first part presents the standard analysis on this subject which supplements, systematizes and advances L. Hospital抯 principles on differential calculus by applying special ,general, and limit guaranteeing theories together with K(t) and XhK0 theories. The combination of theoretical analysis and geometric signification makes the derivation intuitional, visual and easy to perceive.展开更多
Let {qn, } be a sequence of positive integers, and In={0,1,..,qn}. The sequence of random variables {Xn, n0} is called a Cantor-like random sequence if for every n,Xn takes on values in In, and p(X0=x0,…Xn=xn)>0,T...Let {qn, } be a sequence of positive integers, and In={0,1,..,qn}. The sequence of random variables {Xn, n0} is called a Cantor-like random sequence if for every n,Xn takes on values in In, and p(X0=x0,…Xn=xn)>0,The purpose of this paper is to give a strong limit theorem for these sequences.展开更多
The definition of strong limit-point for singular Hamiltonian difference expressions with complex coefficients are given, and some strong limit-point criteria are established.
Subject Code:A04With the support by the National Natural Science Foundation of China,a collaborative study by the research groups led by Profs.Li Wei(李渭),Chen Xi(陈曦)and Xue Qikun(薛其坤)from Tsinghua University an...Subject Code:A04With the support by the National Natural Science Foundation of China,a collaborative study by the research groups led by Profs.Li Wei(李渭),Chen Xi(陈曦)and Xue Qikun(薛其坤)from Tsinghua University and Prof.Shen Zhixun(沈志勋)from Stanford University,demonstrates stripes developed展开更多
Suppose that X ={Xt, t≥0;Pμ} is a supercritical superprocess in a locally compact separable metric space E. Let φ0 be a positive eigenfunction corresponding to the first eigenvalue λ0 of the generator of the mean ...Suppose that X ={Xt, t≥0;Pμ} is a supercritical superprocess in a locally compact separable metric space E. Let φ0 be a positive eigenfunction corresponding to the first eigenvalue λ0 of the generator of the mean semigroup of X. Then Mt := e-λ0t〈φ0,Xt〉 is a positive martingale. Let M∞ be the limit of Mt. It is known(see Liu et al.(2009)) that M∞ is non-degenerate if and only if the L log L condition is satisfied. In this paper we are mainly interested in the case when the L log L condition is not satisfied. We prove that, under some conditions, there exist a positive function γt on [0,∞) and a non-degenerate random variable W such that for any finite nonzero Borel measure μ on E,lim/t→∞γt〈φ0,Xt〉=W, a.s.-Pμ.We also give the almost sure limit of γt〈f, Xt〉for a class of general test functions f.展开更多
It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system ha...It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system has at most two(one) limit cycles which have (1,1) distribution ((0,1) distribution).展开更多
Let (X0,Y0), be i. i. d nonnegative random vectors with continuous survival distribution function be the product-limit estimator of S(s,t) suggested by Campbell and Foldes (1980). In this paper it is shown that under...Let (X0,Y0), be i. i. d nonnegative random vectors with continuous survival distribution function be the product-limit estimator of S(s,t) suggested by Campbell and Foldes (1980). In this paper it is shown that under some conditions a sequence of Gaussian processes Gn(s,t) can be constructed such that sup a. s.,for S,T which together satisfy a certain condition.展开更多
After defining the strong tensor product of strong (sub)chain complenes, it is shown that an analogue of the Kunneth theorem holds in strong homology by proving that the kernel (cokernel) of connecting homomorphisms i...After defining the strong tensor product of strong (sub)chain complenes, it is shown that an analogue of the Kunneth theorem holds in strong homology by proving that the kernel (cokernel) of connecting homomorphisms is isomorphic to the direct sum of torsion (tensor) products of strong homology groups. An isomorphism between strong (r-stage) homology groups of inverse systems is also constructed.展开更多
Most reinforced concrete(RC)frame structures did not achieve the "strong column-weak beam" failure mode in recent big earthquakes, resulting in a large number of casualties and significant property loss. To ...Most reinforced concrete(RC)frame structures did not achieve the "strong column-weak beam" failure mode in recent big earthquakes, resulting in a large number of casualties and significant property loss. To deal with this serious problem, a new column-beam relative factor was proposed to characterize the relative yield situation of column ends and beam ends. By limiting the column-beam relative factor, RC frame structures could achieve the "strong column-weak beam" failure mode under the excitation of strong ground motions. The limit values of column-beam relative factor were calculated, analyzed and verified by using structural simulation models for corner columns in the bottom story of structures, which are destroyed most seriously in earthquakes. The results show that the limit values should be analyzed under bi-directional ground motion and with different axial compression ratios of columns. The peak ground acceleration(PGA)of ground motions has no significant effect on the limit values, while the type of strong ground motions has a significant effect on the limit values.展开更多
In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. wh...In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.展开更多
We consider a discrete time Storage Process Xn with a simple random walk input Sn and a random release rule given by a family {Ux, x ≥ 0} of random variables whose probability laws {Ux, x ≥ 0} form a convolution sem...We consider a discrete time Storage Process Xn with a simple random walk input Sn and a random release rule given by a family {Ux, x ≥ 0} of random variables whose probability laws {Ux, x ≥ 0} form a convolution semigroup of measures, that is, μx × μy = μx + y The process Xn obeys the equation: X0 = 0, U0 = 0, Xn = Sn - USn, n ≥ 1. Under mild assumptions, we prove that the processes and are simple random walks and derive a SLLN and a CLT for each of them.展开更多
基金Supported by the Special Fundation of Tianjin Education Committee(2006ZH91)Supported by the Key Discipline of Applied Mathematics at Tianjin University of Commerce(X0803)
文摘First,a class of strong limit theorems are proved by constructing two nonnegative martingales.Then they are applied to the study of all kinds of even-odd Markov chain fields and Markov chain fields defined in the paper.Finally,some strong limit theorems for the even-odd Markov chain fields and Markov chain fields are obtained.
文摘This in virtue of the notion of likelihood ratio and the tool of moment generating function, the limit properties of the sequences of random discrete random variables are studied, and a class of strong deviation theorems which represented by inequalities between random variables and their expectation are obtained. As a result, we obtain some strong deviation theorems for Poisson distribution and binomial distribution.
基金supported by the National Natural Science Foundation of China(Nos.11571142,11971197,11601191)。
文摘In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class of its equivalent forms.Based on this property,some strong limit theorems including conditional entropy density are studied for the tree-indexed Markov chains in random environment.
文摘Strong and weak limits as well as strong and weak differentials of multi-variable indeterminate forms are discussed based on the thorough exploration of differentiation to solve the strong and weak limits and differentials of unitary indeterminate forms. The fruit of this work is going to be reported in three parts. The first part presents the standard analysis on this subject which supplements, systematizes and advances L. Hospital抯 principles on differential calculus by applying special ,general, and limit guaranteeing theories together with K(t) and XhK0 theories. The combination of theoretical analysis and geometric signification makes the derivation intuitional, visual and easy to perceive.
文摘Let {qn, } be a sequence of positive integers, and In={0,1,..,qn}. The sequence of random variables {Xn, n0} is called a Cantor-like random sequence if for every n,Xn takes on values in In, and p(X0=x0,…Xn=xn)>0,The purpose of this paper is to give a strong limit theorem for these sequences.
基金This research is supported by the Natural Science Foundation of China(10471077)Shandong Research Funds for Young Scientists(03BS094)and National Science Foundation of Educational Department of Shandong Province(03P51)(J04A60).
文摘The definition of strong limit-point for singular Hamiltonian difference expressions with complex coefficients are given, and some strong limit-point criteria are established.
文摘Subject Code:A04With the support by the National Natural Science Foundation of China,a collaborative study by the research groups led by Profs.Li Wei(李渭),Chen Xi(陈曦)and Xue Qikun(薛其坤)from Tsinghua University and Prof.Shen Zhixun(沈志勋)from Stanford University,demonstrates stripes developed
基金supported by National Natural Science Foundation of China (Grant Nos. 11671017, 11731009 and 11601354)Key Laboratory of Mathematical Economics and Quantitative Finance (Peking University), Ministry of Education, the Simons Foundation (Grant No. 429343)Youth Innovative Research Team of Capital Normal University
文摘Suppose that X ={Xt, t≥0;Pμ} is a supercritical superprocess in a locally compact separable metric space E. Let φ0 be a positive eigenfunction corresponding to the first eigenvalue λ0 of the generator of the mean semigroup of X. Then Mt := e-λ0t〈φ0,Xt〉 is a positive martingale. Let M∞ be the limit of Mt. It is known(see Liu et al.(2009)) that M∞ is non-degenerate if and only if the L log L condition is satisfied. In this paper we are mainly interested in the case when the L log L condition is not satisfied. We prove that, under some conditions, there exist a positive function γt on [0,∞) and a non-degenerate random variable W such that for any finite nonzero Borel measure μ on E,lim/t→∞γt〈φ0,Xt〉=W, a.s.-Pμ.We also give the almost sure limit of γt〈f, Xt〉for a class of general test functions f.
文摘It is proved that the quadratic system with a weak focus and a strong focus has at most one limit cycle around the strong focus, and as the weak focus is a 2nd order(or 3rd order) weak focus the quadratic system has at most two(one) limit cycles which have (1,1) distribution ((0,1) distribution).
文摘Let (X0,Y0), be i. i. d nonnegative random vectors with continuous survival distribution function be the product-limit estimator of S(s,t) suggested by Campbell and Foldes (1980). In this paper it is shown that under some conditions a sequence of Gaussian processes Gn(s,t) can be constructed such that sup a. s.,for S,T which together satisfy a certain condition.
文摘After defining the strong tensor product of strong (sub)chain complenes, it is shown that an analogue of the Kunneth theorem holds in strong homology by proving that the kernel (cokernel) of connecting homomorphisms is isomorphic to the direct sum of torsion (tensor) products of strong homology groups. An isomorphism between strong (r-stage) homology groups of inverse systems is also constructed.
基金Supported by the National Natural Science Foundation of China(No.51525803)the Scientific and Technological Development Plans of Tianjin Construction System(No.2013-35)+1 种基金International Science&Technology Cooperation Program of China(No.2012DFA70810)the Basic Science Research Foundation of IEM,CEA(No.2013B07)
文摘Most reinforced concrete(RC)frame structures did not achieve the "strong column-weak beam" failure mode in recent big earthquakes, resulting in a large number of casualties and significant property loss. To deal with this serious problem, a new column-beam relative factor was proposed to characterize the relative yield situation of column ends and beam ends. By limiting the column-beam relative factor, RC frame structures could achieve the "strong column-weak beam" failure mode under the excitation of strong ground motions. The limit values of column-beam relative factor were calculated, analyzed and verified by using structural simulation models for corner columns in the bottom story of structures, which are destroyed most seriously in earthquakes. The results show that the limit values should be analyzed under bi-directional ground motion and with different axial compression ratios of columns. The peak ground acceleration(PGA)of ground motions has no significant effect on the limit values, while the type of strong ground motions has a significant effect on the limit values.
文摘In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.
文摘We consider a discrete time Storage Process Xn with a simple random walk input Sn and a random release rule given by a family {Ux, x ≥ 0} of random variables whose probability laws {Ux, x ≥ 0} form a convolution semigroup of measures, that is, μx × μy = μx + y The process Xn obeys the equation: X0 = 0, U0 = 0, Xn = Sn - USn, n ≥ 1. Under mild assumptions, we prove that the processes and are simple random walks and derive a SLLN and a CLT for each of them.
