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Date Published:
31/03/2023
Abstract Views: 176
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Views PDF: 74
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Section
NATURAL SCIENCES
How to Cite
Nguyễn, N. Q. (2023). Almost surely exponential stability of differential delay equations with stochastic noise. Dong A University Journal of Science, 2(1), 16-25. https://js.donga.edu.vn/index.php/daujs/article/view/132
Almost surely exponential stability of differential delay equations with stochastic noise
Main Article Content
Abstract
In the present paper, we aim to study of a class of nonlinear differential equations with stochastic noise. Firstly, we introduce the condition of local Lipschitz and a new non-linear growth condition. Then by applying Lyapunov function and semi-martingale convergence theorem, we investigate the almost surely exponential stability of solutions
Article Details
Keywords
Stochastic differential equation, stochastic noise, almost surely exponential stability
References
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Zhu, Q. (2014). Asymptotic stability in the pth moment for stochastic differential equations with Lévy noise. Journal of Mathematical Analysis and Applications, 416(1), 126-142.
Zhu, Q. (2017). Razumikhin-type theorem for stochastic functional differential equations with Lévy noise and Markov switching. International Journal of Control, 90(8), 1703-1712.
Zhu, Q. (2018). Stability analysis of stochastic delay differential equations with Lévy noise. Systems & Control Letters, 118, 62-68.
LaSalle, J. P. (1968). Stability theory for ordinary differential equations. Journal of Differential equations, 4(1), 57-65.
Li, C. W., Dong, Z., & Situ, R. (2002). Almost sure stability of linear stochastic differential equations with jumps. Probability theory and related fields, 123(1), 121-155.
Mao, W., You, S., & Mao, X. (2016). On the asymptotic stability and numerical analysis of solutions to nonlinear stochastic differential equations with jumps. Journal of Computational and Applied Mathematics, 301, 1-15.
Mao, X. (1994). Exponential stability of stochastic differential equations. Marcel Dekker.
Zhu, Q. (2014). Asymptotic stability in the pth moment for stochastic differential equations with Lévy noise. Journal of Mathematical Analysis and Applications, 416(1), 126-142.
Zhu, Q. (2017). Razumikhin-type theorem for stochastic functional differential equations with Lévy noise and Markov switching. International Journal of Control, 90(8), 1703-1712.
Zhu, Q. (2018). Stability analysis of stochastic delay differential equations with Lévy noise. Systems & Control Letters, 118, 62-68.