Abstract
This study focuses on the highly nonlinear hybrid neutral stochastic differential equations (NSDEs) with multiple time-dependent delays and different structures. The new stochastic system in this paper contains multiple time-dependent delays in the neutral term, and the coefficients are also with different delay functions in drift and diffusion terms respectively. Besides, the set of Markov switching states are divided into two subsets, and the structures of the system are different in each of them. Firstly, the existence, uniqueness and asymptotic boundedness of the global solution of the new NSDE are proved, and then the novel criteria of pth moment and almost surely exponential stability are investigated. All these results are obtained under highly nonlinear coefficients that satisfy local Lipschitz condition and Khasminskii-type conditions, and the Lyapunov function method and the generalized Itô formula are mainly used. Moreover, the Euler-Maruyama approximate solution is established and proved to be convergent in probability to the theoretical solution. Finally, a numerical example is presented together with the corresponding computer simulation to demonstrate the effectiveness of the main results.
Published Version
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