Numerical solutions of stochastic differential delay equations under local Lipschitz condition

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Existence and uniqueness of the solutions and convergence of semi-implicit Euler methods for stochastic pantograph equations (2007, background): “4) holds [19], but for the convenience of the reader we preserve it.”
Exponential stability of equidistant Euler-Maruyama approximations of stochastic differential delay equations (2007, background): “[6,8,23,24,32,33,35,36]) while the exponential stability is clearly an asymptotic property.”
Stochastic delay differential equations for genetic regulatory networks (2007, methodology): “Based on the progress of efficient methods for simulating SDDEs [2,6,7,14,16], we will use two simple systems to study the impact of time delay on the dynamics of GRNs and discuss the implementations of variable time delays.”