On the stochastic Leontief type equations with variable matrices given in terms of current velocities of the solution

The stochastic Leontief type equations are a particular case of stochastic systems of differential-algebraic type. The paper deals with the study of the system given in terms of current velocities (symmetric derivatives at an average value) of the solution. It should be noted that in a physical meaning the current velocity of stochastic processes is a direct analog of the physical velocity of deterministic process. The authors assume that the matrices of the system under consideration are rectangular time dependants and satisfy the conditions, under which the system is not solvable with respect to the symmetric derivative. In order to investigate the system of equations the authors use an approach based on the transformation of a square matrix to the canonical Jordan form and changing the metric in the space. The theorem on solution existence for stochastic Leontief type equation with current velocities under some additional conditions on its matrices of coefficients and free terms is proved.