  This paper studies the second moment boundedness of solutions of linear
stochastic delay differential equations. First, we give a framework, for
general $\mathrm{N}$-dimensional linear stochastic differential equations with
a single discrete delay, of calculating the characteristic function for the
second moment boundedness. Next, we apply the proposed framework to a special
case of a type of 2-dimensional equation that the stochastic terms are
decoupled. For the 2-dimensional equation, we obtain the characteristic
function explicitly given by equation coefficients, the characteristic function
gives sufficient conditions for the second moment to be bounded or unbounded.
