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数学进展 - 2018, Vol. 47(1): 11-30
Ergodicity of Stochastic Differential Equations Driven by Lévy Noise with Local Lipschitz Coefficients

DONG Yilin

中国科学技术大学数学科学学院, 合肥, 安徽, 230026
School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, P. R. China

出版日期: 2018-01-25
2018, Vol. 47(1): 11-30
DOI: 10.11845/sxjz.2016135b

[227 KB]

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摘要 本文研究了Lévy过程驱动的带局部Lipschitz系数的随机微分方程解的遍历性, 所得的结果可以应用在系数多项式增长的随机动力系统中. 并在文中给出了一些例子.
关键词 遍历性Lévy噪声局部Lipschitz系数Lyapunov函数    
Abstract:In this paper, we study the ergodicity of stochastic differential equations driven by Lévy noise with local Lipschitz coefficients. The result can be applied to the stochastic dynamic systems with polynomial growth coefficients. Some interesting examples are given.
Key wordsergodicity    Lévy noise    local Lipschitz coefficient    Lyapunov function
PACS:  O211.63  
通讯作者: E-mail:   
[1] Bolley, F., Gentil, I. and Guillin, A., Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations,
J. Funct. Anal., 2012, 263(8): 2430-2457.
[2] Chen, L.F., Dong, Z., Jiang, J.F. and Zhai, J.L., On limiting behavior of stationary measures for stochastic evolution systems with small noise intensity, 2016, arXiv: 1611.07223v1 [math.PR].
[3] Da Prato, G. and Zabczyk, J., Ergodicity for Infinite Dimensional Systems, London Math. Soc. Lecture Note Ser., Vol. 229, Cambridge: Cambridge Univ. Press, 1996.
[4] Dong, Z. and Xie, Y.C.,
Ergodicity of stochastic 2D Navier-Stokes equation with Lévy noise, J. Differential Equations, 2011, 251(1): 196-222.
[5] Hairer, M. and Mattingly, J.C., Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing, Ann. of Math. (2}), 2006, 164(3): 993-1032.
[6] Hirsch, M.W., Stability and convergence in strongly monotone dynamical systems, J. Reine Angew. Math., 1988, 383: 1-53.
[7] Khasminskii, R.Z., Stochastic Stability of Differential Equations, Stoch. Model. Appl. Probab., Vol. 66, New York: Springer-Verlag, 2012.
[8] Kupiainen, A., Ergodicity of two dimensional turbulence (after Hairer and Mattingly), In: Séminaire Bourbaki. Vol. 2009/2010, Exposés 1012-1026, Astérisque, No. 339, Paris: Soc. Math. France, 2011, Exp. No. 1016, vii, 137-156.
[9] Zhang, X.C., Exponential ergodicity of non-Lipschitz stochastic differential equations, Proc. Amer. Math. Soc.,
2009, 137: 329-337.
[1] 邵金, 蒋辉. 非时齐扩散过程遍历性的假设检验[J]. 数学进展, 2019, 48(4): 482-488.
[2] 刘凯,邹捷中. 无穷维空间中的Lyapunov函数方法和随机稳定性(英文)[J]. 数学进展, 2000, 29(5): 385-396.
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