Gumbel and Frechet convergence of the maxima of independent random walks
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Gumbel and Frechet convergence of the maxima of independent random walks. / Mikosch, Thomas Valentin; Yslas Altamirano, Jorge.
I: Advances in Applied Probability, Bind 52, Nr. 1, 2020, s. 213-236.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Gumbel and Frechet convergence of the maxima of independent random walks
AU - Mikosch, Thomas Valentin
AU - Yslas Altamirano, Jorge
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
U2 - 10.1017/apr.2019.57
DO - 10.1017/apr.2019.57
M3 - Journal article
VL - 52
SP - 213
EP - 236
JO - Advances in Applied Probability
JF - Advances in Applied Probability
SN - 0001-8678
IS - 1
ER -
ID: 248031364