Алгоритм повышения порядка стационарного стохастического марковского поля на плоскости

Abstract

Предлагается алгоритм построения двухмерного вещественного нормального марковского поля второго порядка, любые ортогональные сечения которого являются стационарными случайными процессами Орнштейна-Уленбека. Показано, что предлагаемый подход позволяет синтезировать марковские случайные поля более высокого порядка. Смоделированы нормальные марковские поля нулевого, первого и второго порядков, реализованные на плоской поверхности двух переменных.

The algorithm for generating random two-dimensional object on the plane is used for modeling the movement of vehicles and consideration of other problems, the solution of which is Markov random field of the second order. Algorithm is synthesized for constructing two-dimensional real normal Markov field of the second order any orthogonal cross-sections of which are stationary stochastic Ornstein-Uhlenbeck process. It is shown that the proposed approach allows the synthesis of Markov random fields of higher o rder. Normal Markov fields of zero, first and second order, realized on the flat surface of two variables, have been modeled. In this article a sequence have been of embedded algorithms for generating random object of normal Markov field synthesized in the second row, any cross section which is orthogonal, are stationary stochastic Ornstein-Uhlenbeck processes, which differential equations are second order or higher. In this article an algorithm describes to increase the order of the random object – normal Markov field, any orthogonal cross sections which are stationary random Ornstein-Uhlenbeck process. Similar statements can be formulated for the fields, which are generated in the amount and in the space of a higher dimension. The reduction in the value of the partial decrements observed smoothing of the generated form field. It is noted that partial decrements additions affect the kind of topography of the gen erated field.