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The author considers a practical algorithm for estimating an unknown parameter of the mathematical model of a Markov process with local interaction based on the Gibbs distribution. It is proposed to apply the stochastic quasi-gradient method to the maximum likelihood function, which is constructed from the observations of the realizations of the Gibbs field. The obtained results have a wide application scope in the modeling of stochastic processes. [ABSTRACT FROM AUTHOR]

The author considers a practical algorithm for estimating an unknown parameter of the mathematical model of a Markov process with local interaction based on the Gibbs distribution. It is proposed to apply the stochastic quasi-gradient method to the maximum likelihood function, which is constructed from the observations of the realizations of the Gibbs field. The obtained results have a wide application scope in the modeling of stochastic processes. [ABSTRACT FROM AUTHOR]

The authors consider an algorithm for estimating the unknown parameters of the infection spread model based on the Markov field tools using the maximum likelihood method. It is assumed that each state of the Markov chain represents some configuration of a finite random Markov field, and the probability distribution of the chain states is the same as general probability distribution of the states of elements of the Gibbs random field. [ABSTRACT FROM AUTHOR]

The paper examines the properties of consistency and asymptotic normality of the maximum likelihood estimate for Markov sequences with Gibbs distribution. Theorems are formulated and proved that allow approximating the criterion function of a Markov process with a unique minimum point by its empirical estimate. The results can be used to analyze the convergence of unknown parameters to their true values. [ABSTRACT FROM AUTHOR]