In this paper we describe a wide class of non-Volterra quadratic stochasticoperators using N. Ganikhadjaev's construction of quadratic stochasticoperators. 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 definedon each maximal connected subgraphs of $G$ then corresponding non-Volterraoperator can be reduced to $m$ number (where $m$ is the number of maximalconnected subgraphs of $G$) of Volterra operators defined on the maximalconnected subgraphs. Our result allows to study a wide class of non-Volterraoperators in the framework of the well known theory of Volterra quadraticstochastic operators.
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机译：在本文中，我们使用N. Ganikhadjaev的二次随机算子的构造来描述一类非Volterra二次随机算子。通过构造，这些算子依赖于在图$ G上给出的所有配置的集合上定义的概率测度$ mu $。我们表明，如果$ mu $是在每个最大值上定义的概率测度的乘积关联的$ G $子图，然后可以将对应的非Volterraoperator减少为在最大关联子图上定义的Volterra运算符的$ m $个数（其中$ m $是$ G $的最大关联子图数）。我们的结果允许在著名的Volterra二次随机算子理论的框架内研究各种各样的非Volterra算子。
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