Super-linear hybrid neutral stochastic differential equations with non-differentiable delay : Hasminskii-type theorems and stability

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Dong, Ran and Bahar, Arifah and Mao, Xuerong (2026) Super-linear hybrid neutral stochastic differential equations with non-differentiable delay : Hasminskii-type theorems and stability. Discrete and Continuous Dynamical Systems - Series B, 31. pp. 498-522. ISSN 1531-3492 (https://doi.org/10.3934/dcdsb.2025119)

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Abstract

This paper was concerned with a class of superlinear hybrid neutral stochastic differential delay equations (NSDDEs). The significant feature was that the time delay functions in the hybrid NSDDEs were no longer required to be differentiable, not to mention that their derivatives had to be less than 1. The generalized Hasminskii-type theorems were established for the existence and uniqueness of the global solutions. In comparison with the existing results, we showed that our new theorems were much more general and could be applied to a much wider class of superlinear hybrid NSDDEs. Further sufficient conditions were also obtained for the long-term properties including boundedness and stability.

ORCID iDs

Dong, Ran, Bahar, Arifah and Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864;
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