N. V. Azbelev's W-method in the theory of linear stochastic functional differential equations

A stochastic version of the W-method, which goes back to N.V. Azbelev and his students, is discussed in the paper. A justification of the suggested version is based on two theorems, which can provide a basis for a general framework for stability analysis of linear stochastic functional differential equations. An example of a scalar Ito equation is provided to demonstrate efficiency of the method.