Stability of Solutions to LinearFunctional-Integral Itô Equations

The paper is devoted to the study of stability of solutions of a new class of linear functionally integral Itô equations, which contains many classical equations, e.g., differential equations of integer and fractional order with and without stochastic perturbations them, as well as some less known and understudied types of equations that have been introduced into scientific circulation recently. The connection between different types of stability of solutions of these equations and belonging of their solutions to the corresponding spaces of random processes. Using this connection sufficient conditions of stability of solutions with respect to initial data in terms of parameters of these equations. The notion of admissibility of pairs of spaces for the above mentioned the notion of admissibility of pairs of spaces for the above mentioned equations and the relationship between admissibility of pairs of spaces and stability with respect to the initial function.