We consider linear delay differential equations at the verge of Hopf instability, i.e. a pair of roots of the characteristic equation are on the imaginary axis of the complex plane and all other roots have negative real parts. When nonlinear and noise perturbations are present, we show that the error in approximating the dynamics of the delay system by certain two dimensional stochastic differential equation without delay is small (in an appropriately defined sense). Two cases are considered: (i) linear perturbations and multiplicative noise (ii) cubic perturbations and additive noise. The approximation results are useful because, processes without delay are easier to simulate numerically as they do not require storage of the history of the process.
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