Consider the positive d-dimensional lattice Z^d（d≥2） with partial ordering ≤, let {XK; K∈Z＋^d} be i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with mean zero and ...Consider the positive d-dimensional lattice Z^d（d≥2） with partial ordering ≤, let {XK; K∈Z＋^d} be i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with mean zero and covariance operator ∑ and set partial sums SN =∑K≤nXK,K,N∈Z＋^d. Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε↓ by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of （Gut and Spataru, 2003）.展开更多
The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a fir...The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. We assume that the variation of the number of active sites has three possibilities in each update： to increase by 1 with probability f1, to decrease by 1 with probability f2, or remain unchanged with probability 1 - f1 - f2. This mimics the dynamics in the system. Power-law distributions of the lifetime are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions.展开更多
Benford＇s law is logarithmic law for distribution of leading digits formulated by P[D=d]= log（1＋1/d） where d is leading digit or group of digits. It＇s named by Frank Albert Benford （1938） who formulated mathema...Benford＇s law is logarithmic law for distribution of leading digits formulated by P[D=d]= log（1＋1/d） where d is leading digit or group of digits. It＇s named by Frank Albert Benford （1938） who formulated mathematical model of this probability. Befbre him, the same observation was made by Simon Newcomb. This law has changed usual preasumption of equal probability of each digit on each position in number.The main characteristic properties of this law are base, scale, sum, inverse and product invariance. Base invariance means that logarithmic law is valid for any base. Inverse invariance means that logarithmic law for leading digits holds for inverse values in sample. Multiplication invariance means that if random variable X follows Benford＇s law and Y is arbitrary random variable with continuous density then XY follows Benford＇s law too. Sum invariance means that sums of significand are the same for any leading digit or group of digits. In this text method of testing sum invariance property is proposed.展开更多
In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of the α-mixing coefficients for sequences of events, under which the conclusion of the Second Bor...In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of the α-mixing coefficients for sequences of events, under which the conclusion of the Second Borel-Cantelli Lemma holds. As corollaries, some moment conditions are obtained, under which the strong law of large numbers holds for sequences of identically distributed random variables.展开更多
A P2P scientific collaboration is a P2P network whose members can share documents, co-compile papers and codes, and communicate with each other instantly. From the simulation experiment we found that P2P collaboration...A P2P scientific collaboration is a P2P network whose members can share documents, co-compile papers and codes, and communicate with each other instantly. From the simulation experiment we found that P2P collaboration system is a power-law network with a tail between -2 and -3.We utilized the algorithm that searches by high-degree shortcuts to improve the scalability of p2p collaboration system. The experimental result shows that the algorithm works better than random walk algorithm.展开更多
Consider a sequence of negatively associated and identically distributed random variableswith the underlying distribution in the domain of attraction of a stable distribution with an exponentin(0,2).A Chover's law...Consider a sequence of negatively associated and identically distributed random variableswith the underlying distribution in the domain of attraction of a stable distribution with an exponentin(0,2).A Chover's law of the iterated logarithm is established for negatively associated randomvariables.Our results generalize and improve those on Chover's law of the iterated logarithm(LIL)type behavior previously obtained by Mikosch(1984),Vasudeva(1984),and Qi and Cheng(1996)fromthe i.i.d,case to NA sequences.展开更多
In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtaine...In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtained. Our results generalize and improve those on almost sure convergence theorems previously obtained by Marcinkiewicz （1937）, Jamison （1965）, Matula （1992） and Wu （2001） from the independent identically distributed （i.i.d.） case to pairwise NQD sequences.展开更多
基金Project (No. 10471126) supported by the National Natural Science Foundation of China
文摘Consider the positive d-dimensional lattice Z^d（d≥2） with partial ordering ≤, let {XK; K∈Z＋^d} be i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with mean zero and covariance operator ∑ and set partial sums SN =∑K≤nXK,K,N∈Z＋^d. Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε↓ by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of （Gut and Spataru, 2003）.
基金The project supported in part by National Natural Science Foundation of China under Grant Nos.10635020 and 10475032the Major Project of the Ministry of Education of China under Grant No.306022.
文摘The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. We assume that the variation of the number of active sites has three possibilities in each update： to increase by 1 with probability f1, to decrease by 1 with probability f2, or remain unchanged with probability 1 - f1 - f2. This mimics the dynamics in the system. Power-law distributions of the lifetime are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions.
文摘Benford＇s law is logarithmic law for distribution of leading digits formulated by P[D=d]= log（1＋1/d） where d is leading digit or group of digits. It＇s named by Frank Albert Benford （1938） who formulated mathematical model of this probability. Befbre him, the same observation was made by Simon Newcomb. This law has changed usual preasumption of equal probability of each digit on each position in number.The main characteristic properties of this law are base, scale, sum, inverse and product invariance. Base invariance means that logarithmic law is valid for any base. Inverse invariance means that logarithmic law for leading digits holds for inverse values in sample. Multiplication invariance means that if random variable X follows Benford＇s law and Y is arbitrary random variable with continuous density then XY follows Benford＇s law too. Sum invariance means that sums of significand are the same for any leading digit or group of digits. In this text method of testing sum invariance property is proposed.
基金Supported by the SCR of Chongqing Municipal Education Commission(KJ090703)
文摘In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of the α-mixing coefficients for sequences of events, under which the conclusion of the Second Borel-Cantelli Lemma holds. As corollaries, some moment conditions are obtained, under which the strong law of large numbers holds for sequences of identically distributed random variables.
文摘A P2P scientific collaboration is a P2P network whose members can share documents, co-compile papers and codes, and communicate with each other instantly. From the simulation experiment we found that P2P collaboration system is a power-law network with a tail between -2 and -3.We utilized the algorithm that searches by high-degree shortcuts to improve the scalability of p2p collaboration system. The experimental result shows that the algorithm works better than random walk algorithm.
基金supported by the National Natural Science Foundation of China under Grant No.10661006the Support Program of the New Century Guangxi China Ten-Hundred-Thousand Talents Project under Grant No.2005214the Guangxi, China Science Foundation under Grant No.2010GXNSFA013120
文摘Consider a sequence of negatively associated and identically distributed random variableswith the underlying distribution in the domain of attraction of a stable distribution with an exponentin(0,2).A Chover's law of the iterated logarithm is established for negatively associated randomvariables.Our results generalize and improve those on Chover's law of the iterated logarithm(LIL)type behavior previously obtained by Mikosch(1984),Vasudeva(1984),and Qi and Cheng(1996)fromthe i.i.d,case to NA sequences.
基金This research is supported by the National Natural Science Foundation of China under Grant No. 11061012, the Support Program of the New Century Guangxi China Ten-hundred-thousand Talents Project under Grant No. 2005214, and the Guangxi, China Science Foundation under Grant No. 2010GXNSFA013120.
文摘In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtained. Our results generalize and improve those on almost sure convergence theorems previously obtained by Marcinkiewicz （1937）, Jamison （1965）, Matula （1992） and Wu （2001） from the independent identically distributed （i.i.d.） case to pairwise NQD sequences.
