Explicit criteria for moment exponential stability and instability of switching diffusions with Lévy noise

References

• Applebaum, D. (2009). Lévy processes and stochastic calculus. Cambridge University Press.
   Google Scholar
• Applebaum, D., & Siakalli, M. (2009). Asymptotic stability of stochastic differential equations driven by Lévy noise. Journal of Applied Probability, 46(4), 1116–1129. https://doi.org/10.1239/jap/1261670692
   Web of Science ®Google Scholar
• Applebaum, D., & Siakalli, M. (2010). Stochastic stabilization of dynamical systems using Lévy noise. Stochastics and Dynamics, 10(04), 509–527. https://doi.org/10.1142/S0219493710003066
   Google Scholar
• Chao, Z., Wang, K., Zhu, C., & Zhu, Y. (2017). Almost sure and moment exponential stability of regime-switching jump diffusions. SIAM Journal on Control and Optimization, 55(6), 3458–3488. https://doi.org/10.1137/16M1082470
   Web of Science ®Google Scholar
• Chen, X., Chen, Z. Q., Tran, K., & Yin, G. (2019). Recurrence and ergodicity for a class of regime-switching jump diffusions. Applied Mathematics & Optimization, 80(2), 415–445. https://doi.org/10.1007/s00245-017-9470-9
   Web of Science ®Google Scholar
• Cont, R., & Tankov, P. (2004). Financial modelling with jump processes. Financial mathematics series. Chapman & Hall/CRC.
   Google Scholar
• Du, N. H., Nguyen, D. H., Nguyen, N. N., & Yin, G. (2021). Stability of stochastic functional differential equations with random switching and applications. Automatica, 125, 109410. https://doi.org/10.1016/j.automatica.2020.109410
   Google Scholar
• Gray, A., Greenhalgh, D., Hu, L., Mao, X., & Pan, J. (2011). A stochastic differential equation SIS epidemic model. SIAM Journal on Applied Mathematics, 71(3), 876–902. https://doi.org/10.1137/10081856X
   Web of Science ®Google Scholar
• Ikeda, N., & Watanabe, S. (2014). Stochastic differential equations and diffusion processes. Elsevier.
   Google Scholar
• Ji, H., Shao, J., & Xi, F. (2020). Stability of regime-switching jump diffusion processes. Journal of Mathematical Analysis and Applications, 484(1), 123727. https://doi.org/10.1016/j.jmaa.2019.123727
   Web of Science ®Google Scholar
• Kou, S. G. (2002). A jump-diffusion model for option pricing. Management Science, 48(8), 1086–1101. https://doi.org/10.1287/mnsc.48.8.1086.166
   Web of Science ®Google Scholar
• Li, X., Gray, A., Jiang, D., & Mao, X. (2011). Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching. Journal of Mathematical Analysis and Applications, 376(1), 11–28. https://doi.org/10.1016/j.jmaa.2010.10.053
   Web of Science ®Google Scholar
• 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. https://doi.org/10.1016/j.cam.2016.01.020
   Web of Science ®Google Scholar
• Mao, X. (1999). Stability of stochastic differential equations with Markovian switching. Stochastic Processes and Their Applications, 79(1), 45–67. https://doi.org/10.1016/S0304-4149(98)00070-2
   Web of Science ®Google Scholar
• Mao, X., & Yuan, C. (2006). Stochastic differential equations with Markovian switching. Imperial College Press.
   Google Scholar
• Shao, J., & Xi, F. (2014). Stability and recurrence of regime-switching diffusion processes. SIAM Journal on Control and Optimization, 52(6), 3496–3516. https://doi.org/10.1137/140962905
   Web of Science ®Google Scholar
• Teel, A. R., Subbaraman, A., & Sferlazza, A. (2014). Stability analysis for stochastic hybrid systems: A survey. Automatica, 50(10), 2435–2456. https://doi.org/10.1016/j.automatica.2014.08.006
   Web of Science ®Google Scholar
• Tran, K., & Yin, G. (2021). Optimal control and numerical methods for hybrid stochastic SIS models. Nonlinear Analysis: Hybrid Systems, 41(772), 101051.
   Google Scholar
• Tran, K. Q. (2021). Exponential contraction of switching jump diffusions with a hidden Markov chain. Statistics & Probability Letters, 178(3), 109191. https://doi.org/10.1016/j.spl.2021.109191
   Google Scholar
• Wu, F., Yin, G., & Wang, L. Y. (2015). Razumikhin-type theorems on moment exponential stability of functional differential equations involving two-time-scale Markovian switching. Mathematical Control & Related Fields, 5(3), 697–719. https://doi.org/10.3934/mcrf.2015.5.697
   Web of Science ®Google Scholar
• Yin, G., & Xi, F. (2010). Stability of regime-switching jump diffusions. SIAM Journal on Control and Optimization, 48(7), 4525–4549. https://doi.org/10.1137/080738301
   Web of Science ®Google Scholar
• Yin, G., & Zhu, C. (2009). Hybrid switching diffusions: properties and applications (Vol. 63). Springer Science & Business Media.
   Google Scholar
• Yuan, C., & Bao, J. (2013). On the exponential stability of switching-diffusion processes with jumps. Quarterly of Applied Mathematics, 71(2), 311–329. https://doi.org/10.1090/qam/2013-71-02
   Web of Science ®Google Scholar
• Zhu, C., Yin, G., & Baran, N. A. (2015). Feynman–Kac formulas for regime-switching jump diffusions and their applications. Stochastics An International Journal of Probability and Stochastic Processes, 87(6), 1000–1032. https://doi.org/10.1080/17442508.2015.1019884
   Web of Science ®Google Scholar
• 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. https://doi.org/10.1080/00207179.2016.1219069
   Web of Science ®Google Scholar
• Zhu, Q., Song, S., & Tang, T. (2017). Mean square exponential stability of stochastic nonlinear delay systems. International Journal of Control, 90(11), 2384–2393. https://doi.org/10.1080/00207179.2016.1249030
   Web of Science ®Google Scholar
• Zong, X., Wu, F., Yin, G., & Jin, Z. (2014). Almost sure and pth-moment stability and stabilization of regime-switching jump diffusion systems. SIAM Journal on Control and Optimization, 52(4), 2595–2622. https://doi.org/10.1137/14095251X
   Web of Science ®Google Scholar