A probability wave description of stochastic variables whose means satisfy a system of difference equations

Probability wave theory is used to study the behavior of stochastic vectors whose means satisfy ordinary first-order difference equations. Difference-differential equations are given for the probability waves corresponding to the difference model for the means. Analogues of the Liouville and Ehrenfest theorems are proved. A first-order difference equation for the evolution of the component dispersion of the random vector is obtained. An algorithm for solving the wave equations is proposed. The results from analyzing some solutions to the probability wave equations are presented. The relationship of the finite-difference method to the manifestation of the particle-wave dualism is discussed. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 115. No. 1, pp. 56–76. April. 1998.