%0 Journal Article
%T Second Moment Boundedness of Linear Stochastic Delay Differential Equations
%A Zhen Wang
%A Xiong Li
%A Jinzhi Lei
%J Statistics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1210.2809v1