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The Stochastic Chafee–Infante Equation

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2085)

Abstract

In this preparatory chapter, the tools of stochastic analysis needed for the investigation of the asymptotic behavior of the stochastic Chafee–Infante equation are provided. In the first place, this encompasses a recollection of basic facts about Lévy processes with values in Hilbert spaces. Playing the role of the additive noise processes perturbing the deterministic Chafee–Infante equation in the systems the stochastic dynamics of which will be our main interest, symmetric α-stable Lévy processes are in the focus of our investigation (Sect. 3.1).

Keywords

  • Mild Solution
  • Exit Time
  • Small Noise
  • Compound Poisson Process
  • Large Jump

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. A. Araujo, A. Giné, On tails and domains of attraction of stable measures in Banach spaces. Trans. Am. Math. Soc. 1, 105–119 (1979)

    CrossRef  Google Scholar 

  2. N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular Variation (Cambridge University Press, Cambridge, 1987)

    CrossRef  MATH  Google Scholar 

  3. G. DaPrato, J. Zabczyk, in Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and Its Applications, vol. 44 (Cambridge University Press, Cambridge, 1992)

    Google Scholar 

  4. H. Hulk, F. Lindskog, Regular variation for measures on metric spaces. Publi. l’Institut de Mathématiques Nouvelle Sér. 80, 94 (2006)

    Google Scholar 

  5. O. Kallenberg, Foundations of Modern Probability, 2nd edn. (2002) (Springer, New York, 1997)

    Google Scholar 

  6. A. Klenke, Wahrscheinlichkeitstheorie, vol. 2. korrigierte Auflage (2008) (Springer, New York, 2005)

    Google Scholar 

  7. S. Peszat, J. Zabczyk, Stochastic Partial Differential Equations with Lévy Noise (an Evolution Equation Approach) (Cambridge University Press, Cambridge, 2007)

    CrossRef  MATH  Google Scholar 

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Debussche, A., Högele, M., Imkeller, P. (2013). The Stochastic Chafee–Infante Equation. In: The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise. Lecture Notes in Mathematics, vol 2085. Springer, Cham. https://doi.org/10.1007/978-3-319-00828-8_3

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