Gumbel and Frechet convergence of the maxima of independent random walks

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We consider point process convergence for sequences of independent and identically distributed random walks. The objective is to derive asymptotic theory for the largest extremes of these random walks. We show convergence of the maximum random walk to the Gumbel or the Fréchet distributions. The proofs depend heavily on precise large deviation results for sums of independent random variables with a finite moment generating function or with a subexponential distribution. © Applied Probability Trust 2020.
Original languageEnglish
JournalAdvances in Applied Probability
Volume52
Issue number1
Pages (from-to)213-236
ISSN0001-8678
DOIs
Publication statusPublished - 2020

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