The limit distribution of the maximum increment of a random   walk with dependent regularly varying jump sizes

Thomas Valentin Mikosch; Martin Moser

doi:10.1007/s00440-012-0427-2

The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes

Thomas Valentin Mikosch, Martin Moser

Department of Mathematical Sciences

1 Citation (Scopus)

Abstract

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.

Original language	English
Journal	Probability Theory and Related Fields
Volume	156
Pages (from-to)	249-272
ISSN	0178-8051
DOIs	https://doi.org/10.1007/s00440-012-0427-2
Publication status	Published - Jun 2013

Access to Document

10.1007/s00440-012-0427-2

https://link.springer.com/content/pdf/10.1007/s00440-012-0427-2.pdf

Cite this

@article{90f99719a62e4a12924554f72dffe8c3,

title = "The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes",

abstract = "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 Fr{\'e}chet distributed random variable.",

author = "Mikosch, {Thomas Valentin} and Martin Moser",

year = "2013",

month = jun,

doi = "10.1007/s00440-012-0427-2",

language = "English",

volume = "156",

pages = "249--272",

journal = "Probability Theory and Related Fields",

issn = "0178-8051",

publisher = "Springer",

}

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 - 2013/6

Y1 - 2013/6

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

SN - 0178-8051

VL - 156

SP - 249

EP - 272

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

ER -