Algorithm for constructing of stationary normal Markov 3d-field: dynamic equations of motion, statistical probability distributions, visualization

Рассмотрено трехмерное поле, обладающее свойствами стационарности, нормальности и марковости. На основе иерархического подхода проведен вероятностный анализ рассматриваемых случайных величин, процессов и полей. Построен и статистически обоснован алгоритм генерации такого поля в параллелепипеде. Приведен численный пример реализации предложенного алгоритма. Построено трехмерное нормальное марковское поле в объеме.A three-dimensional field with properties of stationary, normality and Markov process is considered. In the paper is considered a three-dimensional field, which has the properties of stationarity, normality, and process of Markov. The analysis is based on the equation of motion of the amplitude of a three-dimensional field with a generating three-dimensional field possessing the properties of three-dimensional white noise. For a random variable, the amplitudes of a three-dimensional normal Markov field of the first order in the volume, transition conditional probability density densities are obtained together with the unconditional probability distribution density. On their basis, an algorithm for generating such a field in a parallelepiped is constructed and justified. A numerical example of the implementation of the proposed algorithm is given