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Communications in Statistics - Theory and Methods Volume 48, 2019 - Issue 10
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Original Articles

Ergodicity for population dynamics driven by stable processes with Markovian switching

Jinying TongDepartment of Applied Mathematics, Donghua University, Shanghai, China; View further author information
,
Xuan MaDepartment of Applied Mathematics, Donghua University, Shanghai, China; View further author information
,
Zhenzhong ZhangDepartment of Applied Mathematics, Donghua University, Shanghai, China; Correspondence[email protected]
View further author information
&
Enwen ZhuSchool of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, ChinaView further author information
Pages 2446-2458 | Received 31 Jul 2017, Accepted 05 Apr 2018, Published online: 29 Oct 2018

References

  • Applebaum, D. 2009. Lévy processes and stochastic calculus. 2nd ed. Cambridge, UK: Cambridge University Press.
  • Brockmann, D., L. Hufnagel, and T. Geisel. 2006. The scaling laws of human travel. Nature 439:462–65.
  • Khasminskii, R. 2011. Stochastic stability of differential equations. 2nd ed. Berlin: Springer.
  • Li, X., A. Gray, D. Jiang, and X. Mao. 2011. Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching. Journal of Mathematical Analysis and Applications 376:11–28.
  • Lipster, R. 1980. A strong law of large numbers for local martingales. Stochastics 3:217–28.
  • Luo, Q., and X. Mao. 2007. Stochastic population dynamics under regime switching. Journal of Mathematical Analysis and Applications 334:69–84.
  • Luo, Q., and X. Mao. 2009. Stochastic population dynamics under regime switching II. Journal of Mathematical Analysis and Applications 355:577–93.
  • Mao, X., G. Yin, and C. Yuan. 2007. Stabilization and destabilization of hybrid systems of stochastic differential equations. Automatica 43:264–73.
  • Mao, X., and C. Yuan. 2006. Stochastic differential equations with Markovian switching[M]. London, UK: Imperial College Press.
  • Pinto, C., A. Mendes, and J. Tenreiro. 2012. A review of power laws in real life phenomena. Communications in Nonlinear Science and Numerical Simulation 17:3558–78.
  • Sato, K. 1999. Lévy processes and infinitely divisible distributions. London, UK: Cambridge University Press.
  • Tong, J., X. Jin, and Z. Zhang. 2017. Exponential ergodicity for SDEs driven by α-stable processes with Markovian switching in Wasserstein distances. Potential Analysis. https://doi.org/10.1007/s11118-017-9665-3.
  • Zhang, Z., X. Jin, and J. Tong. 2018. Ergodicity and transience of SDEs driven by α-stable processes with Markov switching. Applicable Analysis 97:1187–1208.
  • Zhang, Z., X. Zhang, and J. Tong. 2017. Exponential ergodicity for population dynamics driven by α-stable processes. Statistics & Probability Letters 125:149–59.

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