Strong limit theorems are established for weighted sums of widely orthant dependent（WOD） random variables. As corollaries, the strong limit theorems for weighted sums of extended negatively orthant dependent（ENOD）...Strong limit theorems are established for weighted sums of widely orthant dependent（WOD） random variables. As corollaries, the strong limit theorems for weighted sums of extended negatively orthant dependent（ENOD） random variables are also obtained, which extend and improve the related known works in the literature.展开更多
In virtue of the notion of likelihood ratio and moment generating function, the limit properties of the sequences of absolutely continuous random variables are studied, and a class of strong limit theorems represented...In virtue of the notion of likelihood ratio and moment generating function, the limit properties of the sequences of absolutely continuous random variables are studied, and a class of strong limit theorems represented by inequalities with random bounds are obtained.展开更多
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
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
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 National Natural Science Foundation of China (Grant No.11271161)
文摘Strong limit theorems are established for weighted sums of widely orthant dependent（WOD） random variables. As corollaries, the strong limit theorems for weighted sums of extended negatively orthant dependent（ENOD） random variables are also obtained, which extend and improve the related known works in the literature.
基金Supported by the National Nature Science Foundation of China (Grant No. 11101014)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20101103120016)+4 种基金the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (Grant No. PHR20110822)Training Programme Foundation for the Beijing Municipal Excellent Talents (Grant No. 2010D005015000002)the Fundamental Research Foundation of Beijing University of Technology (Grant No. X4006013201101)Education Department Science Project of Hebei Province (Grant No. Z2010297)Science Project of Shijiazhuang University of Economics (Grant No. XN0912)
文摘In virtue of the notion of likelihood ratio and moment generating function, the limit properties of the sequences of absolutely continuous random variables are studied, and a class of strong limit theorems represented by inequalities with random bounds are obtained.
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.
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.
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.
基金Supported by the NNSF of China (10871001, 60803059)Provincial Natural Science Research Project of Anhui Colleges (KJ2010A005)+2 种基金Talents Youth Fund of Anhui Province Universities (2010SQRL016ZD)Youth Science Research Fund of Anhui University (2009QN011A)Academic innovation team of Anhui University (KJTD001B)
