Burkholder Inequalities in Riesz spaces

In this paper, the extent to which the Burkholder Inequalities in classical Stochastic Analysis can be generalized to the new Theory of Stochastic Analysis in Riesz spaces.     

随机环境中马氏链的大数定律和强大数定律

本文主要研究了单无限马氏环境中马氏链的几类特殊函数的大数定律及强大数定律,并且给出了加于链和过程特殊样本函数上的充分条件.     

ψ-混合序列的强大数律

对ψ混合序列，该文得到了强大数律成立的一个必要条件，且对混合速度无任何限制．     

Prokhorov Blocks and Strong Law of Large Numbers Under Rearrangements

We find conditions on a sequence of random variables to satisfy the strong law of large numbers (SLLN) under a rearrangement. It turns out that these conditions are necessary and sufficient for the permutational SLLN (PSLLN). By PSLLN we mean that the SLLN holds under almost all simple permutations within blocks the lengths of which grow exponentially (Prokhorov blocks). In the case of orthogonal random variables it is shown that Kolmogorov's condition, that is known not to be sufficient for SLLN, is actually sufficient for PSLLN. It is also shown that PSLLN holds for sequences that are strictly stationary with finite first moments. In the case of weakly stationary sequences a Gaposhkin result implies that SLLN and PSLLN are equivalent. Finally we consider the case of general norming and generalization of the Nikishin theorem. The methods of proof uses on the one hand the idea of Prokhorov blocks and Garsia's construction of product measure on the space of simple permutations, and on the other hand, a maximal inequality for permutations.     

关于任意随机序列的一个强大数定理

This note is devoted to introduce a new concept of conditionally dominated random variables.Under suitable restrict conditions,a general strong law of large numbers for arbitrary continuous random variables is obtained.     

两两NQD列的强大数定律

该文把同分布的两两NQD列的Kolmogorov强大数定律推广到了在一类广泛的条件下的不同分布的情形, 为此而建立的Kolmogorov Chung型强大数定律本身也是有意义的.      

关于~*-mixing随机变量序列的强大数定律

利用任意随机变量序列的强大数定律讨论 * -mixing随机变量序列的强大数定律 ,得到了该序列的一个强极限定理 ,推广了经典的 * mixing随机变量序列的强大数定律 .同时讨论了 m相依序列和独立随机变量序列的强大数定律 .     

马氏过程函数的强大数定律

本文主要研究了马氏过程函数以及马氏环境中马氏链函数的强大数定律．     

强大数定律的若干新结果

本文利用Hajek-Renyi型最大值不等式,获得了随机变量和的强大数定律和 收敛速度.作为应用,给出了某些相依随机变量和新的强大数定律.     

END序列强大数律研究

本文研究了END序列的均值强大数律,获得了均值强大数律的充分条件. 作为应用,我们可以立即得到Marcinkiewicz均值和logarithmic均值强大数律.最后我们开展了有关大数定律的数据模拟工     

两两NQD序列部分和的强大数定律

By using the moment inequality, maximal inequality and the truncated method of random variables, we establish the strong law of large numbers of partial sums for pairwise NQD sequences, which extends the corresponding result of pairwise NQD random variables.     

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Strong laws of large numbers play key role in nonadditive probability theory. Recently, there are many research papers about strong laws of large numbers for independently and identically distributed (or negatively dependent) random variables in the framework of nonadditive probabilities (or nonlinear expectations). This paper introduces a concept of weakly negatively dependent random variables and investigates the properties of such kind of random variables under aframework of nonadditive probabilities and sublinear expectations. A strong law of large numbers is also proved for weakly negatively dependent random variables under a kind of sublinear expectation as an application     

A Random Set Extension of a Strong Law of Large Numbers of Cantrell and Rosalsky

Abstract

A strong law of large numbers under conditions irrespective of the joint distribution of the sequence is extended to random sets. The extension is such that the role of events of the form {||V _n || ≤ b _n } (where V _n is a random element of a separable Banach space) is played by events of the form {X _n  ? B _n } (where X _n is a random closed bounded set).     

关于弱大数定律的一些讨论

用一个简洁的方法证明了契比雪夫不等式,并就大数定律充分必要条件进行了详细的讨论.证明方法独特新颖.     

Riesz product spaces and representation theory

Let {E _i:i∈I} be a family of Archimedean Riesz spaces. The Riesz product space is denoted by ∏ _i∈I E_i. The main result in this paper is the following conclusion: There exists a completely regular Hausdorff spaceX such that ∏ _i∈I E_i is Riesz isomorphic toC(X) if and only if for everyi∈I there exists a completely regular Hausdorff spaceX _i such thatE _i is Riesz isomorphic toC(X _i). Supported by the National Natural Science Foundation of China     

The Law of Large Numbers and the Ito-Nisio Theorem for Vector Valued Random Fields

Strong convergence results are obtained for vector-valued random fields. Substantial development of Banach-valued random fields and summability results is needed to provide the framework for the major results since many plausible extensions fail for multi-indexed Banach-valued random variables. This development yields general convergence results for random fields in Banach spaces, including an Ito-Nisio theorem and strong laws of large numbers.     

Spitzer's Strong Law of Large Numbers in Nonseparable Banach Spaces

It is well known, that for the sums of i.i.d. random variables we have S _n/n 0 a.s. iff _n=1 1/n P(|S _n| > n) < holds for all > 0 (Spitzer's SLLN). The result is also known in separable Banach spaces. It will be shown, that this also holds in nonseparable (= not necessarily separable) Banach spaces without any measurability assumption. In the theory of empirical processes this gives a characterization of Glivenko-Cantelli classes.     

Strong Laws of Large Numbers for Sublinear Expectation under Controlled 1st Moment Condition

This paper deals with strong laws of large numbers for sublinear expectation under controlled 1st moment condition. For a sequence of independent random variables, the author obtains a strong law of large numbers under conditions that there is a control random variable whose 1st moment for sublinear expectation is finite. By discussing the relation between sublinear expectation and Choquet expectation, for a sequence of i.i.d random variables, the author illustrates that only the finiteness of uniform 1st moment for sublinear expectation cannot ensure the validity of the strong law of large numbers which in turn reveals that our result does make sense.     

Polynomials on Riesz spaces

In this paper we investigate polynomial mappings on Riesz spaces. We give a characterization of positivity of homogeneous polynomials in terms of forward differences. Finally we prove Hahn-Banach type extension theorems for positive and regular polynomial mappings.