A Hájek-Rényi-type maximal inequality and strong laws of large numbers for multidimensional arrays.
Uniform attractors for nonautonomous parabolic equations involving weighted p-Laplacian operators
We consider the first initial boundary value problem for nonautonomous quasilinear degenerate parabolic equations involving weighted p-Laplacian operators, in which the nonlinearity satisfies the polynomial condition of arbitrary order and the external force is normal. Using the asymptotic a priori estimate method, we prove the existence of uniform attractors for this problem. The results, in particular, improve some recent ones for nonautonomous p-Laplacian equations.
Strong laws of large numbers for sequences of blockwise and pairwise -dependent random variables in metris spaces
The aim of the paper is to establish strong laws of large numbers for sequences of blockwise and pairwise -dependent random variables in a convex combination space with or without compactly uniformly integrable condition. Some of our results are even new in the case of real random variables.
The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces
We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.
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