On Non-Volterra Quadratic Stochastic Operators Generated by a Product Measure
Open Access
- 24 February 2009
- journal article
- research article
- Published by Taylor & Francis Ltd in Stochastic Analysis and Applications
- Vol. 27 (2), 353-362
- https://doi.org/10.1080/07362990802678994
Abstract
In this article, 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 μ being defined on the set of all configurations which are given on a graph G. We show that if μ 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.Keywords
This publication has 9 references indexed in Scilit:
- Map of fixed points and Lyapunov functions for one class of discrete dynamical systemsMathematical Notes, 1994
- QUADRATIC STOCHASTIC OPERATORS, LYAPUNOV FUNCTIONS, AND TOURNAMENTSSbornik: Mathematics, 1993
- A TOPOLOGICAL APPROACH TO A PROBLEM IN MATHEMATICAL GENETICSRussian Mathematical Surveys, 1979
- ON THE BEHAVIOUR OF TRAJECTORIES AND THE ERGODIC HYPOTHESIS FOR QUADRATIC MAPPINGS OF A SIMPLEXRussian Mathematical Surveys, 1978
- Gibbs States on Countable SetsPublished by Cambridge University Press (CUP) ,1974
- BASIC CONCEPTS AND THEOREMS OF THE EVOLUTIONARY GENETICS OF FREE POPULATIONSRussian Mathematical Surveys, 1971
- A General Model for the Genetic Analysis of Pedigree DataHuman Heredity, 1971
- Quadratic differential systems for interactive population modelsJournal of Differential Equations, 1969
- Genetic Algebras Studied Recursively and by Means of Differential Operators.MATHEMATICA SCANDINAVICA, 1962