A Unified Approach to Limit Theorems in Probability Theory and Its Application
In this paper, we show a convergence behavior of a general class of Borel functions of random variables. Our motivation for this paper is to use this convergence behavior to unify some of the existing important limit theorems, which are available in the literature as independent theorems. To achieve this we derive a general limit theorem in a function space of probability distributions. The special cases of the main theorem includes generalized
central limit theorem, extremal types theorem and limit theorems of random sum, random maxima and random minima. We derive the limit theory of extremes under nonlinear normalization as a special case of the main result. We show the limit theory of product of i.i.d.r.v of fixed sample sizes and random sample sizes as special cases of the main theorem. Moreover, we show how the main theorem can be useful to derive some of the new
limit theorems in probability.
Disclaimer/Regarding indexing issue:
We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.