Stability of stochastic differential-algebraic equations with delay

Abstract

The aim of this paper is to study solvability and stability of stochastic differential-algebraic equations (SDAEs) with delay. It is difficult to investigate these properties for SDAEs with delay because of the singularity of the leading coefficient matrix. An index-ν concept is derived for solvability of these equations. Stability of SDAEs with delay is studied by using the method of Lyapunov functions and comparison principle. An example is given to illustrate the results. To the best of our knowledge, these results are novel for SDAEs with delay.