Analysis and Probability

Chapter 10

Sums of Independent Random Variables

Sums of independent random variables have already been encountered in the preceding chapter as row sums of arrays of random variables. On the basis of results therefrom, in Section 25 we deepen the study of weak convergence to zero of such sums, leading to the so-called weak laws of large numbers. Starting with Section 26 we investigate almost sure behavior of (stabilized) sums , of independent random variables . The stochastic process lies at the heart of classical and modern probability theory. In ...