This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Bayer, ChristianHoel, Hakonvon Schwerin, ErikTempone, Raúl2016-03-242019-06-2820130946-8633https://doi.org/10.34657/2819https://oa.tib.eu/renate/handle/123456789/1629We consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. The performance of a typical second moment based sequential stopping rule MC method is shown to be unreliable in such settings both by numerical examples and through analysis. By analysis and approximations, we construct a higher moment based stopping rule which is shown in numerical examples to perform more reliably and only slightly less efficiently than the second moment based stopping rule.application/pdfeng510Monte Carlo methodsoptimal stoppingsequential stopping rulesnon-asymptoticReport