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Stability of stochastic differential equations with Markovian switching

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Cited by:

  1. Li, Jin & Guo, Ying & Liu, Xiaotong & Zhang, Yifan, 2024. "Stabilization of highly nonlinear stochastic coupled systems with Markovian switching under discrete-time state observations control," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
  2. Taras Lukashiv, 2016. "One Form of Lyapunov Operator for Stochastic Dynamic System with Markov Parameters," Journal of Mathematics, Hindawi, vol. 2016, pages 1-5, September.
  3. E. K. Boukas, 2004. "Nonfragile Controller Design for Linear Markovian Jumping Parameters Systems," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 241-255, August.
  4. Yang Li & Taitao Feng & Yaolei Wang & Yifei Xin, 2021. "A High Order Accurate and Effective Scheme for Solving Markovian Switching Stochastic Models," Mathematics, MDPI, vol. 9(6), pages 1-15, March.
  5. Li, Yuyuan & Lu, Jianqiu & Kou, Chunhai & Mao, Xuerong & Pan, Jiafeng, 2018. "Robust discrete-state-feedback stabilization of hybrid stochastic systems with time-varying delay based on Razumikhin technique," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 152-161.
  6. You, Surong & Hu, Liangjian & Mao, Wei & Mao, Xuerong, 2015. "Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 8-16.
  7. Rujivan, Sanae & Thamrongrat, Nopporn & Juntanon, Parun & Djehiche, Boualem, 2025. "Analytical computation of conditional moments in the extended Cox–Ingersoll–Ross process with regime switching: Hybrid PDE system solutions with financial applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 176-202.
  8. Tran, Ky Quan, 2021. "Exponential contraction of switching jump diffusions with a hidden Markov chain," Statistics & Probability Letters, Elsevier, vol. 178(C).
  9. You, Surong & Mao, Wei & Mao, Xuerong & Hu, Liangjian, 2015. "Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 73-83.
  10. Wenhai Qi & Yonggui Kao & Xianwen Gao, 2017. "Further results on finite-time stabilisation for stochastic Markovian jump systems with time-varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(14), pages 2967-2975, October.
  11. Song, Gongfei & Zhang, Zimeng & Zhu, Yanan & Li, Tao, 2022. "Discrete-time control for highly nonlinear neutral stochastic delay systems," Applied Mathematics and Computation, Elsevier, vol. 430(C).
  12. E. K. Boukas, 2008. "On State Feedback Stabilization of Singular Systems with Random Abrupt Changes," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 335-345, May.
  13. Yue-Chao Ma & Yang-Fan Liu & Hui Chen, 2017. "Reliable finite-time control of uncertain singular nonlinear Markovian jump systems with bounded transition probabilities and time-varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(11), pages 2249-2261, August.
  14. Khasminskii, R.Z. & Zhu, C. & Yin, G., 2007. "Stability of regime-switching diffusions," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1037-1051, August.
  15. Mao, Xuerong & Shen, Yi & Yuan, Chenggui, 2008. "Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1385-1406, August.
  16. Rathinasamy, Anandaraman & Nair, Priya, 2018. "Asymptotic mean-square stability of weak second-order balanced stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential systems," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 276-303.
  17. Wensheng Luo & Ruifang Zhang & Jianwen Zhang & Ligang Wu & Sergio Vazquez & Leopoldo G. Franquelo, 2024. "Control of Three-Phase Two-Level Inverters: A Stochastic LPV Model Approach," Energies, MDPI, vol. 17(23), pages 1-16, December.
  18. Xi, Fubao, 2004. "Stability of a random diffusion with nonlinear drift," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 273-286, July.
  19. Ma, Yuechao & Chen, Hui, 2015. "Reliable finite-time H∞ filtering for discrete time-delay systems with Markovian jump and randomly occurring nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 897-915.
  20. Xi, Fubao & Yin, G., 2010. "Asymptotic properties of nonlinear autoregressive Markov processes with state-dependent switching," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1378-1389, July.
  21. Zhang, Jianyu & Wang, Yingying & Yang, Songwei & Li, Jiaojiao & Qu, Hao, 2024. "A design of fuzzy sliding mode control for Markovian jumping system with different input matrices," Applied Mathematics and Computation, Elsevier, vol. 463(C).
  22. Zhezhe Xin & Chunjie Xiao & Ting Hou & Xiao Shen, 2019. "Robust H ∞ -Control for Uncertain Stochastic Systems with Impulsive Effects," Mathematics, MDPI, vol. 7(12), pages 1-12, December.
  23. Socha, Leslaw & Zhu, Quanxin, 2019. "Exponential stability with respect to part of the variables for a class of nonlinear stochastic systems with Markovian switchings," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 2-14.
  24. E. K. Boukas, 2004. "Nonfragile Robust Controller for Linear Markovian Jumping Parameter Systems with Multiplicative Brownian Disturbance," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 455-469, September.
  25. Qian, Wei-Liang & F. Siqueira, Adriano & F. Machado, Romuel & Lin, Kai & Grant, Ted W., 2017. "Dynamical capacity drop in a nonlinear stochastic traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 328-339.
  26. Xu, Ruiping & Kao, Yonggui & Gao, Cunchen, 2015. "Exponential synchronization of delayed Markovian jump complex networks with generally uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 682-693.
  27. Peng Shi & Yanyan Yin & Fei Liu, 2013. "Gain-Scheduled Worst-Case Control on Nonlinear Stochastic Systems Subject to Actuator Saturation and Unknown Information," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 844-858, March.
  28. Siqueira, Adriano F. & Peixoto, Carlos J.T. & Wu, Chen & Qian, Wei-Liang, 2016. "Effect of stochastic transition in the fundamental diagram of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 87(C), pages 1-13.
  29. Li, Bing, 2017. "A note on stability of hybrid stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 45-57.
  30. Guo, Beibei & Xiao, Yu, 2024. "Synchronization of multi-link and multi-delayed inertial neural networks with Markov jump via aperiodically intermittent adaptive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 435-453.
  31. Luo, Jiaowan & Liu, Kai, 2008. "Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(5), pages 864-895, May.
  32. Xu, Guangli & Wang, Yongjin, 2016. "On stability of the Markov-modulated skew CIR process," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 139-144.
  33. Liang, Tiantian & Shi, Shengli & Ma, Yuechao, 2023. "Asynchronous sliding mode control of continuous-time singular markov jump systems with time-varying delay under event-triggered strategy," Applied Mathematics and Computation, Elsevier, vol. 448(C).
  34. Ruan, Dehao & Xu, Liping & Luo, Jiaowan, 2019. "Stability of hybrid stochastic functional differential equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 832-841.
  35. Wang, Xingxing & Ma, Yuechao, 2023. "Adaptive non-fragile sliding mode control for switched semi-Markov jump system with time-delay and attack via reduced-order method," Applied Mathematics and Computation, Elsevier, vol. 440(C).
  36. Wei Hu, 2022. "Stability of Impulsive Stochastic Delay Systems with Markovian Switched Delay Effects," Mathematics, MDPI, vol. 10(7), pages 1-12, March.
  37. Tran, Ky Q. & Le, Bich T.N., 2022. "On exponential stability of non-autonomous stochastic differential equations with Markovian switching," Statistics & Probability Letters, Elsevier, vol. 189(C).
  38. Zhou, Jianping & Sang, Chengyan & Li, Xiao & Fang, Muyun & Wang, Zhen, 2018. "H∞ consensus for nonlinear stochastic multi-agent systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 41-58.
  39. Zhao, Ping & Feng, Wei & Zhao, Yan & Kang, Yu, 2015. "Finite-time stochastic input-to-state stability of switched stochastic nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1038-1054.
  40. Fan, Zhencheng, 2017. "Convergence of numerical solutions to stochastic differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 176-187.
  41. Yuan, Chenggui & Mao, Xuerong, 2003. "Asymptotic stability in distribution of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 277-291, February.
  42. Yuan, Chenggui & Mao, Xuerong, 2004. "Convergence of the Euler–Maruyama method for stochastic differential equations with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(2), pages 223-235.
  43. Xu, Jiang & Chen, Tao & Wen, Xiangdan, 2021. "Analysis of a Bailey–Dietz model for vector-borne disease under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
  44. Zhou, Qi & Yao, Deyin & Wang, Jiahui & Wu, Chengwei, 2016. "Robust control of uncertain semi-Markovian jump systems using sliding mode control method," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 72-87.
  45. T. Senthilkumar & P. Balasubramaniam, 2011. "Delay-Dependent Robust Stabilization and H ∞ Control for Nonlinear Stochastic Systems with Markovian Jump Parameters and Interval Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 100-120, October.
  46. Xinghu Jin & Tian Shen & Zhonggen Su & Yuzhen Tan, 2025. "The Euler-Maruyama Approximation of State-Dependent Regime Switching Diffusions," Journal of Theoretical Probability, Springer, vol. 38(1), pages 1-40, March.
  47. Obradović, Maja, 2019. "Implicit numerical methods for neutral stochastic differential equations with unbounded delay and Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 664-687.
  48. Yingqi Zhang & Yan Shi & Xiaowu Mu & Caixia Liu, 2017. "control for conic non-linear jump systems with partially unknown transition probabilities," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(14), pages 2976-2984, October.
  49. Ye, Zhiyong & Zhang, He & Zhang, Hongyu & Zhang, Hua & Lu, Guichen, 2015. "Mean square stabilization and mean square exponential stabilization of stochastic BAM neural networks with Markovian jumping parameters," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 156-165.
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