Let $\{S_n\}$ be the partial sums of a sequence of independent random variables and let $\{a_n\}$ be a nondecreasing, divergent real sequence. Necessary and sufficient conditions for $\lim ...

Stein's method has emerged as a critical framework in the study of distributional approximations, providing quantitative bounds between probability distributions through the formulation and solution ...

It is shown that under fairly mild conditions linear combinations of independent normally distributed random variables with random coefficients tend to zero almost everywhere. The result is applied to ...