IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v68y2004i3p273-286.html
   My bibliography  Save this article

Stability of a random diffusion with nonlinear drift

Author

Listed:
  • Xi, Fubao

Abstract

For the solution to a rather general nonlinear stochastic differential equation with Markovian switching, we first prove its Feller continuity and the existence and uniqueness of invariant measure by the coupling method, then discuss its stability in total variation norm by the Foster-Lyapunov inequality.

Suggested Citation

  • Xi, Fubao, 2004. "Stability of a random diffusion with nonlinear drift," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 273-286, July.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:3:p:273-286
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(04)00104-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xi, Fubao, 2009. "Asymptotic properties of jump-diffusion processes with state-dependent switching," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2198-2221, July.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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).
    3. 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.
    4. 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.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:68:y:2004:i:3:p:273-286. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.