TL;DR
This paper extends a classical probability lemma to establish strong limit results for the maxima of sequences, providing a deeper understanding of their convergence behavior.
Contribution
It generalizes the Borel-Cantelli lemma and applies this to derive new strong convergence results for maxima sequences.
Findings
Established a generalized Borel-Cantelli lemma.
Derived strong limit theorems for maxima sequences.
Enhanced understanding of maxima convergence in probability theory.
Abstract
In the present paper, a generalization of the first part of the Borel-Cantelli lemma is obtained by the recent work of Balakrishnan and Stepanov (2010). This generalization is further applied to derive strong limit results for the sequence of maxima.
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Mathematical Dynamics and Fractals · Nonlinear Partial Differential Equations