Ergodicity of linear SPDE driven by Lévy noise (original) (raw)

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References

  1. D. Barbu and B. Gheorghe, Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients, Czechoslovak Math. J., 2002, 52(127): 87–95.
    Article MATH MathSciNet Google Scholar
  2. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, 1992.
  3. G. Da Prato and J. Zabczyk, Ergodicity for Infinite Dimensional Systems, Cambridge University Press, 1996.
  4. G. Da Prato, A. Debussche, and G. Beniamin, Some properties of invariant measures of non symmetric disspative stochstic systems, Probab. Theory Related Fields, 2002, 123: 355–380.
    Article MATH MathSciNet Google Scholar
  5. Y. Liu and H. Z. Zhao, Reprensentation of pathwise staionary solutions of stochastic Burgers’ equations, Stochastics and Dynamics, 2009, 9(4): 613–634.
    Article MATH Google Scholar
  6. R. Mikulevicius, H. Pragarauskas, On Cauchy-Dirichlet problem for parabolic quasilinear SPDEs, Potential Analysis, 2006, 25: 37–75.
    Article MATH MathSciNet Google Scholar
  7. R. Mikulevicius, H. Pragarauskas, and N. Sonnadara, On the Cauchy-Dirichlet problem in the half space for parabolic SPDEs in weighted Hoelder spaces, Acta Appl. Math., 2007, 97: 129–149.
    Article MATH MathSciNet Google Scholar
  8. S. E. A. Mohammed, T. S. Zhang, and H. Z. Zhao, The stable manifold theorem for semilinear stochastic evolution equations and stochastic partial differenial equations, Memoirs of the American Mathematical Society, 2006.
  9. Y. Xie, Existence and uniqueness of solutions of SPDE with non-Lipschitz and non-time-homogeneous coefficients, J. Xuzhou Norm. Univ. Nat. Sci. Ed., 2007, 25(1): 1–5.
    MATH MathSciNet Google Scholar
  10. S. Albeverio, J. L. Wu, and T. S. Zhang, Parabolic SPDEs driven by Poisson white noise, Stochastic Process. Appl., 1998, 74(1): 21–36.
    Article MATH MathSciNet Google Scholar
  11. D. Applebauam and J. L. Wu, Stochastic partial differential equations driven by Lévy space-time white noise, Random Oper. Stochastic Equations, 2000, 8(3): 245–259.
    Article MathSciNet Google Scholar
  12. Z. Dong, The uniqueness of invariant measure of the Burgers equation driven by Lévy processes, Journal of Theoretical Probability, 2008, 21(2): 322–335.
    Article MATH MathSciNet Google Scholar
  13. Z. Dong and Y. Xie, Global solutions of stochastic 2D Navier-Stokes equations with Lévy Noise, Science in China Series A: Mathematics, 2009, 52(7): 1–29.
    Article MathSciNet Google Scholar
  14. Z. Dong and T.G. Xu, One-dimensional stochastic burgers equation driven by Lévy processes, Journal Functional Analysis, 2007, 243: 631–678.
    Article MATH MathSciNet Google Scholar
  15. E. Hausenblas, SPDEs driven by Poisson random measure with non Lipschitz coefficients: existence results, Probab. Theory Related Fields, 2007, 137: 161–200.
    Article MATH MathSciNet Google Scholar
  16. Erwan Saint Loubert Bié, Étude d’une EDPS conduite par un bruit poissonnien, Probability Theory and Related Fields, 1998, 111(2): 287–321.
    Article MATH MathSciNet Google Scholar
  17. A. Truman and J. L. Wu, On a stochastic nonlinear eqnation arising from 1D integro-differential scalar conservation laws, Journal of Functional Analysis, 2006, 238: 612–635.
    MATH MathSciNet Google Scholar
  18. A. Truman and J. L. Wu, Stochastic Burgers equation with Lévy space-time white noise, Probabilistic Methods in Fluids, proceedings of the Swansea 2002 workshop.
  19. Sandra Cerrai, Second Order PDE’s in Finite and Infinite Demension, springer-Verlag Berlin Heidelberg, 2001.
  20. J. Robinson, Infinite-Dimensional Dynamical Systems, Cambridge University Press, 2001.
  21. F. Flandoli and B. Maslowski, Ergodicity of the 2-D Navier-Stokes equation under random perturbations, Commun. Math. Phys., 1995, 171: 119–141.
    Article MathSciNet Google Scholar
  22. B. Ferrario, Ergodic results for stochastic Navier-Stokes equation, Stochastics and Stochastics Reports, 1997, 60: 271–288.
    MATH MathSciNet Google Scholar
  23. G. Da Prato, Kolmogorov Equations for Stochastic PDEs, Birkhäuser Verlag, 2004.

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