Michael Högele (Univ. de los Andes, Kolumbien)
In this talk we present a quantitative version of the Borel-Cantelli lemma, which allows for a quantification of the "tradeoff" between a.s. rates of convergence and the precise integrability of the overshoot count. This allows to quantify the a.s. convergence in different settings, such as the strong law of large number, a large deviations principle and the a.s. martingale convergence in many different situations. Important examples are the a.s. convergence of M-estimators and Polya urns.
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