Forward and backward in time Cauchy problems for systems of parabolic-type PDE with a small parameter

The paper introduces a class of functions where the resolving operator for a system of Kolmogorov–Feller‐type equations with a small parameter is well posed in forward and backward times. The introduced class of functions is invariant under the resolving operator if the solution is understood in the weak sense with an exponential weight. The paper continues the study of .