Second Moment Boundedness of Linear Stochastic Delay Differential   Equations
  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. 
Zhen Wang, Xiong Li, Jinzhi Lei
math.ST math.DS stat.TH