A strong law of large numbers for fuzzy random variables

A limit of a sequence of fuzzy numbers is defined and its some properties are shown. Based on these concept and properties, an independent sequence of fuzzy random variables is considered and a strong law of large numbers for fuzzy random variables is shown.     

The strong law of large numbers for pairwise negatively dependent random variables

Necessary and sufficient conditions for the validity of the strong law of large numbers for pairwise negatively dependent random variables with infinite means are formulated.     

关于M值随机序列的一个普遍成立的强大数定理

利用区间剖分法构造几乎处处收敛的鞅,得到了一个对任意M-值随机变量序列普遍成立的强极限定理,作为推论得到一个精细的Borel—Cantelli引理．     

Kolmogorov's strong law of large numbers for fuzzy random variables

In this paper, Kolmogorov's strong law of large numbers for sums of independent and level-wise identically distributed fuzzy random variables is obtained.     

Some remarks on the strong law of large numbers for Banach-space valued weakly integrable random variables

The purpose of this paper is to show the equivalence of almost sure convergence of S_n/n, n ≥ 1 and lim sup_n→∞S_n/n < ∞ a.e., where S_n = X₁ + X₂ + … + X_n and X₁, X₂,… are independent identically distributed random elements in a separable Banach space with EX₁ < ∞. This result disproves a result of Pop-Stojanovic [8].     

Exponential inequalities for associated random variables and strong laws of large numbers

Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. For the case of geometrically decreasing covariances, we obtain the rate of convergence n-1/2(log log n)1/2(logn) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n-1/3(logn)2/3 and n-1/3(logn)5/3, separately.     

A strong limit theorem for generalized Cantor-like random sequences

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A mixed random walk on nonnegative matrices: A law of large numbers

In this paper a mixed random walk on nonnegative matrices has been studied. Under reasonable conditions, existence of a unique invariant probability measure and a law of large numbers have been established for such walks.     

Inequalities and strong laws of large numbers for random allocations

Summary Moment inqualities and strong laws of large numbers are proved for random allocations of balls into boxes. Random broken lines and random step lines are constructed using partial sums of i.i.d. random variables that are modified by random allocations. Functional limit theorems for such random processes are obtained.     

Strong law of large number for branching hunt processes

In this paper,we prove that,under certain conditions,a strong law of large number holds for a class of branching particle systems X corresponding to the parameters(Y,β,ψ),where Y is a Hunt process andψis the generating function for the offspring.The main tool of this paper is the spine decomposition and we only need an L log L condition.     

On the strong law of large numbers for functionals of countable nonhomogeneous Markov chains

We prove a strong law of large numbers for functionals of nonhomogeneous Markov chains. The approach is analytic and different from the usual one.     

A remark on strong law of large numbers for weighted U-statistics

Let {X,Xn; n ≥ 1} be a sequence of i.i.d.random variables with values in a measurable space(S,S) such that E|h(X1,X2,...,Xm)| ∞,where h is a measurable symmetric function from Sminto R =(-∞,∞).Let {wn,i1,i2,...,im; 1 ≤ i1 i2 ··· im ≤ n,n ≥ m} be a matrix array of real numbers.Motivated by a result of Choi and Sung(1987),in this note we are concerned with establishing a strong law of large numbers for weighted U-statistics with kernel h of degree m.We show that lim n→∞m!(n-m)!n!1≤i1i2···im≤n wn,i1,i2,...,im(h(Xi1,Xi2,...,Xim)-θ)=0 a.s.whenever supn≥mmax1≤i1i2···im≤n|wn,i1,i2,...,im|∞,whereθ=Eh(X1,X2,...,Xm).The proof of this result is based on a new general result on complete convergence,which is a fundamental tool,for array of real-valued random variables under some mild conditions.     

隐非齐次马尔可夫模型的强大数定律

在状态集都有限的情况下,给出了隐马尔可夫模型的一些性质定理．利用马氏链的强极限定理,得到了隐非齐次马尔可夫模型的强大数定律．     

Equivalent conditions of complete convergence for m-dimensional products of iid random variables and application to strong law of large numbers

Under very weak condition 0 × r(f) ↑ ∞, t→ ∞, we obtain a series of equivalent conditions of complete convergence for maxima of m-dimensional products of iid random variables, which provide a useful tool for researching this class of questions. Some results on strong law of large numbers are given such that our results are much stronger than the corresponding result of Gadidov’s.     

An application of rosenthal's moment inequality to the strong law of large numbers

We apply a moment inequality of H.P. Rosenthal to get various generalizations of a theorem of Brunk-Chung-Prohoroff. In particular, we show that the strong law hols provided $\text{∑}\text{n=1}\text{∞}\text{n}{}^{\mathrm{?2p}}\text{E(X}{}_{\mathrm{n}}\text{}{}^{\mathrm{2p}}\text{) < ∞}$ and $\text{∑}\text{n=1}\text{∞}\text{n}{}^{\mathrm{?2?p}}\text{(E(}\text{X}\text{n}\text{2}\text{))}{}^{\mathrm{p}}\text{< ∞}$ for one p ? 1.     

Weak law of large numbers for almost periodically correlated processes

This note contains two simple observations concerning the weak law of large numbers for almost periodically correlated processes.

     

Strong law of large numbers for pair-wise extended lower/upper negatively dependent random variables

We establish some strong limit theorems for a sequence of pair-wise extended lower/upper negatively dependent random variables and give some new examples of dependent random variables.     

Law of large numbers for increasing subsequences of random permutations

Let the random variable Z_n,k denote the number of increasing subsequences of length k in a random permutation from S_n, the symmetric group of permutations of {1,…,n}. We show that Var(Z) = o((EZ)²) as n → ∞ if and only if . In particular then, the weak law of large numbers holds for Z if ; that is, We also show the following approximation result for the uniform measure U_n on S_n. Define the probability measure μ on S_n by where U denotes the uniform measure on the subset of permutations that contain the increasing subsequence {x₁,x₂,…,x}. Then the weak law of large numbers holds for Z if and only if where ∣∣˙∣∣ denotes the total variation norm. In particular then, (*) holds if . In order to evaluate the asymptotic behavior of the second moment, we need to analyze occupation times of certain conditioned two‐dimensional random walks. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006