An improvement of the “quotient construction” method and further asymptotic results on the stationary distributions of the Markov chains modeling evolutionary algorithms

In earlier work of the first author, a method has been presented for analysis of Markov chains modeling evolutionary algorithms through use of a suitable quotient construction. Asymptotic bounds for the rate of concentration of the stationary distribution of the Markov chains modeling evolutionary algorithms have been obtained. The bounds obtained in the previous work involve the increase of selection pressure depending on the decaying mutation rate. The rate of concentration of the stationary distribution of the Markov chain in the reverse order (i.e. decay of mutation rate with respect to the increase in selection pressure) remained an open question. We address this question in the current paper. More informative results obtained with the use of the "quotient construction" method will appear in the sequel papers.