We provide a permutation invariant version of the strong law large numbers for exchangeable sequences random variables. The proof consists combination Komlós–Berkes theorem, usual sequences, and de Finetti’s theorem.

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 20 February 2020Accepted: 29 June 2020Published online: 06 May 2021Keywordscubature, quadrature, quasi--Monte Carlo, randomized simulation-optimizationAMS Subject Headings65D32, 65C05Publication DataISSN (print): 0036-1445ISSN (online): 1095-7200Publisher: Society for Ind...

We prove two variants of Kolmogorov’s strong law of large numbers in a completely worst-case framework, eschewing any probabilistic assumptions. The first variant is an assertion about a game involving the Bookmaker predicting the values of unprobabilized random variables; in an intuitive sense it is much stronger than the usual strong law of large numbers for martingales. The second variant is...

Let X;Xn, n ≥ 1, be a sequence of independent identically distributed random variables. We give necessary and sufficient conditions for the strong law of large numbers n−k/p ∑ 1≤i1 x• as x → ∞, without further conditi...