Multi-dimensional characteristic functions application to the description of nonmarkov random processes

The stochastic differential systems are described with application of the multidimensional characteristic functions. The equations for twodimensional characteristic functions are obtained and their generalization for n-dimensional characteristic functions is made. The elaborated method is applied so as to give a more precise definition of the Brownian motion. It is shown that the method leads to the results coinciding with that obtained before by means of using the method of multi-dimensional distribution functions.