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In this paper estimates for the \(L_\infty \)-norm of solutions of parabolic SPDEs are derived. The result is obtained through iteration techniques, motivated by the work of Moser in deterministic settings. As an application of the main result, solvability of a class of semilinear SPDEs is established.

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The authors would like to express their gratitude towards their PhD advisor, Professor István Gyöngy, for his help and support during the preparation of this paper. They are furthermore grateful to the anonymous referee for her/ his helpful suggestions.

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Correspondence to Konstantinos Dareiotis.

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Dareiotis, K., Gerencsér, M. On the boundedness of solutions of SPDEs. Stoch PDE: Anal Comp 3, 84–102 (2015).

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