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Stability of regime-switching diffusions

Author

Listed:
  • Khasminskii, R.Z.
  • Zhu, C.
  • Yin, G.

Abstract

This work is devoted to stability of regime-switching diffusion processes. After presenting the formulation of regime-switching diffusions, the notion of stability is recalled, and necessary conditions for p-stability are obtained. Then main results on stability and instability for systems arising in approximation are presented. Easily verifiable conditions are established. An example is examined as a demonstration. A remark on linear systems is also provided.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:8:p:1037-1051
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    References listed on IDEAS

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    1. 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.
    2. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    3. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
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    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Threshold of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 614-625.
    3. Alessandro Ramponi, 2011. "Mixture Dynamics and Regime Switching Diffusions with Application to Option Pricing," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 349-368, June.
    4. Zu, Li & Jiang, Daqing & O’Regan, Donal & Hayat, Tasawar & Ahmad, Bashir, 2018. "Ergodic property of a Lotka–Volterra predator–prey model with white noise higher order perturbation under regime switching," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 93-102.
    5. 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.
    6. Quan Wang & Li Zu & Daqing Jiang & Donal O’Regan, 2023. "Study on Dynamic Behavior of a Stochastic Predator–Prey System with Beddington–DeAngelis Functional Response and Regime Switching," Mathematics, MDPI, vol. 11(12), pages 1-17, June.
    7. Caraballo, Tomás & Settati, Adel & Fatini, Mohamed El & Lahrouz, Aadil & Imlahi, Abdelouahid, 2019. "Global stability and positive recurrence of a stochastic SIS model with Lévy noise perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 677-690.
    8. Leonardo Videla & Rolando Rebolledo, 2022. "Evolving Systems of Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1662-1705, September.
    9. Wang, Liang & Jiang, Daqing & Feng, Tao, 2022. "Threshold dynamics in a stochastic chemostat model under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    10. Lin Hu & Lin-Fei Nie, 2022. "Dynamics of a Stochastic HIV Infection Model with Logistic Growth and CTLs Immune Response under Regime Switching," Mathematics, MDPI, vol. 10(19), pages 1-20, September.
    11. 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.
    12. 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.
    13. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Stationary distribution of a regime-switching predator–prey model with anti-predator behaviour and higher-order perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 199-210.
    14. Chen, Zhewen & Tian, Zhuyan & Zhang, Shuwen & Wei, Chunjin, 2020. "The stationary distribution and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    15. Settati, A. & Lahrouz, A. & Zahri, M. & Tridane, A. & El Fatini, M. & El Mahjour, H. & Seaid, M., 2021. "A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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