Purpose. To create models which allow carrying out the allocation of funds from the equity tax in the structure of "region" - "Mining municipality" in due form. Methodology. An approach to create models with the property change adaptation operating conditions is proposed. The approach is based on the analytical apparatus of the theory of stochastic automata operating in random environments and allows formally describing the behaviour of the agent in a measurable uncertainty created by revenues from taxes to the budgets of the lower levels of the budget system of the Russian Federation. Findings. The design of stochastic automation exhibiting property of appropriateness of behaviour and asymptotic optimality is proposed. The machine adapts well to fluctuations in the external environment caused by variations in tax revenues in the budgets of mining municipal entities. We construct the matrix of the automation transition from one state to another under the influence of the input signals, identifying favourable and unfavourable reactions of the environment to the outputs of the machine. Expressions for the final probabilities of the machine stay in their states are obtained. The constructed mathematical models in the form of a probabilistic automaton are used in the decision support system for the management of inter-budgetary control for depressed areas, among which mining municipalities are listed. Originality. The urgent task of creating a model tool contributing to the domination of the stimulating function of budgetary control over the levelling function in the "region" - "Mining municipality" structure. An automation model for the formalization of a certain proportion of taxes in the order of the budget management allocation is developed. The advantage of the model is its adaptability to the conditions of uncertainty of effects of the environment, as well as the capacity for self-training due to the properties of appropriateness of behaviour and asymptotic optimality. Practical value. The practical value of the research is in the application of the constructed models as part of a decision support system in the "region" - "Mining municipality" structure.

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