Stability analysis for nonlinear Markov jump neutral stochastic functional differential systems

Abstract Recently, the asymptotic stability for Markov jump stochastic functional differential systems (SFDSs) was studied, whose stability criteria relied on the intervals lengths of continuous delays. Whereas, so far all the existing references require the rigorous global Lipschitz condition for the delay parts of the drift coefficients and do not consider the challenging factors of exponential decay and neutral issue. Motivated by the aforementioned considerations and the advantages of the degenerate functionals, this paper aims to weaken the global Lipschitz condition for the delay parts of the drift coefficients and investigate the delay-dependent exponential stability and asymptotic boundedness for highly nonlinear Markov jump neutral SFDSs with the method of multiple degenerate functionals. Of course, the delay-independent assertions are as well derived here.