It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we study an interpolation problem in this setting. A key tool is the principle of permanence of algebraic identities.
D. Alpay and H. Attia. An interpolation problem for functions with values in a commutative ring. Operator Theory: Advances and Applications, Vol. 218 (2012), pp. 1-17.