Abstract
This chapter deals with semilinear stochastic evolution equations in Hilbert spaces. The first two sections are more introductory and review some important properties of Wiener processes and the stochastic Itô integral in Hilbert spaces. The main references for the presented material are Da Prato and Zabczyk (Stochastic Equations in Infinite Dimensions, vol. 44, 1992) and Prévôt and Röckner (A Concise Course on Stochastic Partial Differential Equations, vol. 1905, 2007).
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Kruse, R. (2014). Stochastic Evolution Equations in Hilbert Spaces. In: Strong and Weak Approximation of Semilinear Stochastic Evolution Equations. Lecture Notes in Mathematics, vol 2093. Springer, Cham. https://doi.org/10.1007/978-3-319-02231-4_2
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DOI: https://doi.org/10.1007/978-3-319-02231-4_2
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