On Non-Volterra Quadratic Stochastic Operators Generated by a Product Measure

Abstract

In this paper we describe a wide class of non-Volterra quadratic stochastic operators using N. Ganikhadjaev's construction of quadratic stochastic operators. By the construction these operators depend on a probability measure $\mu$ being defined on the set of all configurations which are given on a graph $G.$ We show that if $\mu$ is the product of probability measures being defined on each maximal connected subgraphs of $G$ then corresponding non-Volterra operator can be reduced to $m$ number (where $m$ is the number of maximal connected subgraphs of $G$) of Volterra operators defined on the maximal connected subgraphs. Our result allows to study a wide class of non-Volterra operators in the framework of the well known theory of Volterra quadratic stochastic operators.