Communications of the
Korean Mathematical Society CKMS

This paper investigates mean square exponential dissipativity of singularly perturbed stochastic delay differential equations. The $L$-operator delay differential inequality and stochastic analysis technique are used to establish sufficient conditions ensuring the mean square exponential dissipativity of singularly perturbed stochastic delay differential equations for sufficiently small $\varepsilon>0$. An example is presented to illustrate the efficiency of the obtained results.

Keywords: delay, stochastic, singularly perturbed, mean square exponential dissipativity, $L$-operator delay differential inequality

MSC numbers: 34K50, 34K20, 34K26