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Stochastics and Stochastic Reports Volume 60, 1997 - Issue 1-2
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Original Articles

Exponential stability of stochastic differential delay equations

Xuerong Mao Department of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, Scotland, UK
&
Anita Shah Department of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, Scotland, UK
Pages 135-153 | Published online: 02 May 2007

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Xuekang Zhang, Haoran Yi & Huisheng Shu. (2020) Stabilization and destabilization of nonlinear stochastic differential delay equations. Stochastics 92:1, pages 124-139.
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Osman Tunç & Cemil Tunç. (2019) On the asymptotic stability of solutions of stochastic differential delay equations of second order. Journal of Taibah University for Science 13:1, pages 875-882.
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Yong Liang & Qihong Chen. (2019) Khasminskii-type theorems for stochastic differential delay equations driven by G-Brownian motion. Systems Science & Control Engineering 7:3, pages 104-111.
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Fuke Wu & Shigeng Hu. (2009) Suppression and stabilisation of noise. International Journal of Control 82:11, pages 2150-2157.
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Anandaraman Rathinasamy & Pichamuthu Mayavel. (2023) The balanced split step theta approximations of stochastic neutral Hopfield neural networks with time delay and Poisson jumps. Applied Mathematics and Computation 455, pages 128129.
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John A.D. Appleby & Emmet Lawless. (2023) Mean square asymptotic stability characterisation of perturbed linear stochastic functional differential equations. Applied Numerical Mathematics.
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Anandaraman Rathinasamy & Pichamuthu Mayavel. (2023) Strong convergence and almost sure exponential stability of balanced numerical approximations to stochastic delay Hopfield neural networks. Applied Mathematics and Computation 438, pages 127573.
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Linglong Du & Xinyun Zhou. (2023) The stochastic delayed Cucker-Smale system in a harmonic potential field. Kinetic and Related Models 16:1, pages 54.
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. (2022) Model order reduction for (stochastic-) delay equations with error bounds. Journal of Computational Dynamics 9:4, pages 575-600.
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Arzu Ahmadova, Nazim I. Mahmudov & Juan J. Nieto. (2022) Exponential stability and stabilization of fractional stochastic degenerate evolution equations in a Hilbert space: Subordination principle. Evolution Equations and Control Theory 11:6, pages 1997.
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Yanqiang Chang & Huabin Chen. (2022) Stability analysis of stochastic delay differential equations with Markovian switching driven by Lévy noise. Discrete and Continuous Dynamical Systems - B 27:10, pages 5935.
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CHUONG LUONG & NIKOLAI DOKUCHAEV. (2016) MODELING DEPENDENCY OF VOLATILITY ON SAMPLING FREQUENCY VIA DELAY EQUATIONS. Annals of Financial Economics 11:02, pages 1650007.
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E. Gershon & U. Shaked. (2014) H  ∞  preview tracking control of retarded state-multiplicative stochastic systems . International Journal of Robust and Nonlinear Control 24:15, pages 2119-2135.
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Wenli Zhu, Jiexiang Huang & Zhao Zhao. (2014) Exponential Stability of Stochastic Systems with Delay and Poisson Jumps. Mathematical Problems in Engineering 2014, pages 1-10.
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Wenli Zhu, Jiexiang Huang, Xinfeng Ruan & Zhao Zhao. (2014) Exponential Stability of Stochastic Differential Equation with Mixed Delay. Journal of Applied Mathematics 2014, pages 1-11.
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Jin Fang Han. (2013) Mean-Square Exponential Stability of Stochastic Interval Cellular Neural Networks with Time-Varying Delay. Advanced Materials Research 760-762, pages 1742-1747.
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Wenli Zhu, Xinfeng Ruan, Ye Qin & Jie Zhuang. (2013) Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay. Mathematical Problems in Engineering 2013, pages 1-9.
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Lu Xu & Weiping Yan. (2012) STOCHASTIC FITZHUGH-NAGUMO SYSTEMS WITH DELAY. Taiwanese Journal of Mathematics 16:3.
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E. Gershon & U. Shaked. (2010) Robust H ∞ output‐feedback control of retarded state‐multiplicative stochastic systems . International Journal of Robust and Nonlinear Control 21:11, pages 1283-1296.
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Jin-Fang Han, Shu-Tian Wang & Qin Ma. (2011) Exponential stability of stochastic interval neural networks with multi-delay. Exponential stability of stochastic interval neural networks with multi-delay.
Eli Gershon, Nadav Berman & Uri Shaked. (2011) Robust polytopic H<inf>&#x221E;</inf> control of linear retarded state-multiplicative stochastic systems. Robust polytopic H<inf>&#x221E;</inf> control of linear retarded state-multiplicative stochastic systems.
Joris Bierkens. (2010) Pathwise Stability of Degenerate Stochastic Evolutions. Integral Equations and Operator Theory 69:1, pages 1-27.
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E. Gershon, U. Shaked & N. Berman. (2010) H<inf>&#x221E;</inf> preview tracking control for retarded stochastic systems. H<inf>&#x221E;</inf> preview tracking control for retarded stochastic systems.
Jin-fang Han, Ji-qing Qiu, Hui-ran Jia & Xiang-ting Meng. (2010) Robust stability for stochastic interval Hopfield neural networks with time delays. Robust stability for stochastic interval Hopfield neural networks with time delays.
Weiping Yan, Yong Li & Shuguan Ji. (2010) Random attractors for first order stochastic retarded lattice dynamical systems. Journal of Mathematical Physics 51:3.
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Jin-fang Han & Ji-qing Qiu. (2009) Exponential Stability of a Class of Stochastic Interval Cellular Neural Networks. Exponential Stability of a Class of Stochastic Interval Cellular Neural Networks.
Jinfang Han & Zhiyong Liu. (2009) Exponential Stability of Stochastic Interval Cellular Neural Networks. Exponential Stability of Stochastic Interval Cellular Neural Networks.
Tapan Saha & M. Banerjee. (2009) Effect of small time delay in a predator-prey model within random environment. Differential Equations and Dynamical Systems 16:3, pages 225-250.
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E. Gershon, U. Shaked & N. Berman. (2007) $H_\infty$ Control and Estimation of Retarded State-Multiplicative Stochastic Systems. IEEE Transactions on Automatic Control 52:9, pages 1773-1779.
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W. Q. Zhu. (2006) Nonlinear Stochastic Dynamics and Control in Hamiltonian Formulation. Applied Mechanics Reviews 59:4, pages 230-248.
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Xiaohua Ding. (2006) Exponential stability of a kind of stochastic delay difference equations. Discrete Dynamics in Nature and Society 2006, pages 1-9.
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Xiaolin Li & Jinde Cao. 2005. Advances in Neural Networks — ISNN 2005. Advances in Neural Networks — ISNN 2005 162 167 .
John A.D. Appleby & David W. Reynolds. (2003) Non-exponential stability of scalar stochastic Volterra equations. Statistics & Probability Letters 62:4, pages 335-343.
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John Appleby & Alan Freeman. (2003) Exponential Asymptotic Stability of Linear Itô-Volterra Equation with Damped Stochastic Perturbations. Electronic Journal of Probability 8:none.
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TomÁs Caraballo, Kai Liu & Aubrey Truman. (2000) Stochastic functional partial differential equations: existence, uniqueness and asymptotic decay property. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 456:1999, pages 1775-1802.
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Chuong Luong & Nikolai Dokuchaev. (2014) Modelling Dependency of Volatility on Sampling Frequency via Delay Equations. SSRN Electronic Journal.
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