The goal of the paper is to establish a necessary and sufficient condition for the mean square asymptotic stability of a linear scalar stochastic differential equation with time-depending delay using a fixed point theorem approach.
Reviewer’s remarks: However, there are inconsistencies in the paper which makes it hard to understand.
1) The reviewer guesses that in (2.1), (2.2) is meant to be negative, otherwise the space is not well defined. On the other hand, if, for instance, as in example 3.1, then and (as ) as required; but , therefore .
2) If the Banach space consists of the processes with as , then .
Usually mean asymptotic square stability means
and (mean square stability) together with