An Introduction to Probability Theory and Its Applications, Volume II

TL;DR: Based on a stochastic extension of Karamata’s theory of slowly varying functions, necessary and sufficient conditions are established for weak laws of large numbers for arbitrary linear combinations of independent and identically distributed nonnegative random variables.

TL;DR: In this paper, the authors present the Banach space representation for the set of random finite-dimensional vectors with exponential decreasing tails of distributions, and show that there are at last three types of these multidimensional Banach spaces, i.e., exponential Orlicz spaces, Young spaces and Grand Lebesgue spaces.

TL;DR: Two characteristic methods for data propagation are presented: the first performs a local, greedy optimization to minimize the number of data transmissions needed, while the second creates probabilistically optimized redundant data transmissions to trade off energy efficiency with fault tolerance.

TL;DR: This work proposes an algorithm that uses regression models at query time to assess whether a row of the matrix can enter the top-k set given that only a subset of its values are known and considers prior information about the values in the hidden matrix.