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

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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

Mikosch, TV & Moser, M 2013, 'The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes', Probability Theory and Related Fields, bind 156, s. 249-272. https://doi.org/10.1007/s00440-012-0427-2

APA

Mikosch, T. V., & Moser, M. (2013). The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes. Probability Theory and Related Fields, 156, 249-272. https://doi.org/10.1007/s00440-012-0427-2

Vancouver

Mikosch TV, Moser M. The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes. Probability Theory and Related Fields. 2013;156:249-272. https://doi.org/10.1007/s00440-012-0427-2

Author

Mikosch, Thomas Valentin ; Moser, Martin. / The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes. I: Probability Theory and Related Fields. 2013 ; Bind 156. s. 249-272.

Bibtex

@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",
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",

}

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