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).
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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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DOI: https://doi.org/10.1007/978-3-319-00828-8_3
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Online ISBN: 978-3-319-00828-8
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