Central limit theorem for certain classes of dependent random variables

Our main interest in this article is the central limit theorem (CLT) for dependent classes of random variables. We computed the exact difference between the characteristic function of the sum of dependent random variables and the characteristic function of the sum of independent random variables of the same distributions. The obtained difference serves for defining the class of dependent random variables such that usual convergence in distribution to the normally distributed random variable holds. The dependency structure; as defined in our class of random variables, can be reflected in some physical phenomena.