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Cloud-computing shares a common pool of resources across customers at a scale that is orders of magnitude larger than traditional multi-user systems. Constituent physical compute servers are allocated...
It is shown that Teicher's version of the strong law of large numbers for random variables, taking values in separable Banach spaces, holds under the assumption that the weak law of large numbers h...
Let f be a random variable with values in a metric space (X, d). For some class of metric spaces we define in terms of the metric d mathematical expectation of f as a closed bounded and non-empty s...
For partial sums {S,) of a stationary ergodic sequence {X,} with zero mean we find conditions for m ny-'Pr {sup (S Jk) > E ] < m n= 1 k?n in terms of the strong mixing weficients {a,,) and moment...
We prove the Marcinkiewicz-Zygmund SLLN (MZ- -SLLN) of order p, ~ € 1 12,[ , br associated sequences, not necessarily stationary. Our assumption on the moment of the random variables is minimal. We...
We present the Marcinkiewicz-type strong law of large numbers for random fields {X,, n E Zd,) of pairwise independent random variables, where Zd,, d & 1, is the set of positive d-dimensional lattic...
For a sequence of random elements {G, n 2 1) taking values in a real separable Rademacher type p (1 < p < 2) Banach space and positive constants b,l 7 co, conditions are provided for the strong law...
We use our maximum inequality for p-th order random variables (p>1) to prove a strong law of large numbers (SLLN) for sequences of p-th order random variables. In particular, in the case p=2 our resu...
In the paper we define the convergence of compact fuzzy sets as a convergence of -cuts in the topology of compact subsets of a metric space. Furthermore we define typical convergences of fuzzy vari...
In this paper, we provide a necessary and sufficient condition for general d-dimensional arrays of random variables to satisfy strong law of large numbers. Then, we apply the result to obtain some str...

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