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The Law of Large Numbers for U-statistics Under Absolute Regularity
Law of large numbers U-statistics absolute regularity
2009/5/8
We prove the law of large numbers for U-statistics whose underlying sequence of random variables satisfies an absolute regularity condition ($beta$-mixing condition) under suboptimal conditions.
A Weak Law of Large Numbers for the Sample Covariance Matrix
Law of large numbers,affine normalization sample covariance domain of attraction generalized domain of attraction
2009/5/4
In this article we consider the sample covariance matrix formed from a sequence of independent and identically distributed random vectors from the generalized domain of attraction of the multivariate ...
On the Zero-One Law and the Law of Large Numbers for Random Walk in Mixing Random Environment
Random walk random environment zero-one law law of large numbers
2009/4/24
We prove a weak version of the law of large numbers for multi-dimensional finite range random walks in certain mixing elliptic random environments. This already improves previously existing results, w...