Published: 15 April 2016
Relevance and purpose. The successful solution of many problems of the development of public-territorial formations were determined by results of balancing the budgets at all levels of the budget system, directly correlated with the improvement of the budgetary federalism, which is manifested through the system of interbudgetary relations. A fundamental component of the system of interbudgetary relations is intergovernmental regulation. The mechanisms of budgetary control aims at efcient alignment of level of budgetary security of municipalities while maintaining the interest of local governments in developing their tax base. The effectiveness of the solution of this problem requires application of economic-mathematical methods, models, tools. The aim of the research described in this article, is the creation of adaptive, learning mathematical models of decision support for equity the distribution of taxes between levels of budgetary system The materials and methods. Based on the creation of mathematical models based on the principles of controllability, trainability, adaptability and development. The implementation of these principles implemented by means of the mathematical apparatus of the theory of stochastic automata operating in random environments.Results. The structure of the stochastic automaton obtained a formal expression for the nal probability of the automatic stay in their States.Conclusions. Built automaton model due to the properties of the appropriateness of behavior and asymptotic optimality are able to adapt to variations of environmental effects caused by the receipts in the budget from taxes.