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

Institut for Matematiske Fag

1 Citationer (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.

Originalsprog	Engelsk
Tidsskrift	Probability Theory and Related Fields
Vol/bind	156
Sider (fra-til)	249-272
ISSN	0178-8051
DOI	https://doi.org/10.1007/s00440-012-0427-2
Status	Udgivet - jun. 2013

Adgang til dokumentet

10.1007/s00440-012-0427-2

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

Citationsformater

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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.

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