This paper surveys some results in stochastic differential delay equations beginning with ”On stationary solutions of a stochastic differential equations” by K. Ito and M. Nisio, 1964, and also some results in stochastic stability beginning with the ”Stability of positive supermartingales” by R. Bucy, 1964. The problems discussed in this survey are the existence and uniqueness of solutions of s...

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This paper is concerned with the exponential stability of singularly perturbed delay differential equations with a bounded (state-independent) lag. A generalized Halanay inequality is derived in Section 2, and in Section 3 a sufficient condition will be provided to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is exponentially stable...