| Abstract: | The aim of this work is to introduce a new approach in normal approximations, approximations of semigroups of operators, and approximations by accompanying laws. We describe the method and provide several examples showing how the method works. Loosely speaking, the approach is based on multiplicative representations of differences to estimate. The method considerably reduces the technical part of proofs compared to the traditional approaches. In probability theory, it nicely applies to the nonidentically distributed case; another advantage of the method is its extendability to the case of dependent random variables. |
