Abstract
This chapter contains a concise introduction to the “semigroup (or mild solution) approach”. One difference to the variational approach is that we do not use a Gelfand triple, but just our Hilbert space H. The main idea is to use the linear part (if there is one) of the drift as a “smoothing device”.
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Da Prato, G., Zabczyk, J.: Stochastic Equations in Infinite Dimensions. Encyclopedia of Mathematics and Applications. Cambridge University Press, Cambridge (1992) [see also Second Edition 2014]
Da Prato, G., Zabczyk, J.: Ergodicity for Infinite-Dimensional Systems. London Mathematical Society Lecture Note Series, vol. 229. Cambridge University Press, Cambridge (1996)
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Liu, W., Röckner, M. (2015). Mild Solutions. In: Stochastic Partial Differential Equations: An Introduction. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-22354-4_6
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DOI: https://doi.org/10.1007/978-3-319-22354-4_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22353-7
Online ISBN: 978-3-319-22354-4
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