Cumulants theory and applications are extended

The theory of cumulants is extended introducing a new mathematical tool which is called the “Grinberg bracket”. The bracket of n-th order includes two rows of terms; the bottom row of n base terms and the top row of (n-1) coupling coefficients. The Grinberg bracket is expanded in a linear polynomial of the base terms and coupling coefficients. The algorithm of calculation and the properties of the brackets are defined. The cumulant is a particular case of the Grinberg bracket, when all coupling coefficients are unities. The Grinberg brackets can be successfully used for description of ladder circuits which include transformers