The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes. / Mikosch, Thomas Valentin; Moser, Martin.
I: Probability Theory and Related Fields, Bind 156, 2013, s. 249-272.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes
AU - Mikosch, Thomas Valentin
AU - Moser, Martin
PY - 2013
Y1 - 2013
N2 - We investigate the maximum increment of a random walk with heavy-tailed jump size distribution. Here heavy-tailedness is understood as regular variation of the finite-dimensional distributions. The jump sizes constitute a strictly stationary sequence. Using a continuous mapping argument acting on the point processes of the normalized jump sizes, we prove that the maximum increment of the random walk converges in distribution to a Fréchet distributed random variable.
AB - We investigate the maximum increment of a random walk with heavy-tailed jump size distribution. Here heavy-tailedness is understood as regular variation of the finite-dimensional distributions. The jump sizes constitute a strictly stationary sequence. Using a continuous mapping argument acting on the point processes of the normalized jump sizes, we prove that the maximum increment of the random walk converges in distribution to a Fréchet distributed random variable.
U2 - 10.1007/s00440-012-0427-2
DO - 10.1007/s00440-012-0427-2
M3 - Journal article
VL - 156
SP - 249
EP - 272
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
SN - 0178-8051
ER -
ID: 46001650