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Titel:

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

Dokumenttyp:
Zeitschriftenaufsatz
Autor(en):
Mikosch, T., and Moser, M.
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.
Stichworte:
Maximum increment of a random walk, dependent jump sizes; moving average process; GARCH process; stochastic volatility model; regular variation, extreme value distribution
Zeitschriftentitel:
Probability Theory and Related Fields
Jahr:
2013
Band / Volume:
156
Heft / Issue:
1-2
Seitenangaben Beitrag:
249-272
Reviewed:
ja
Sprache:
en
Volltext / DOI:
doi:10.1007/s00440-012-0427-2
Status:
Verlagsversion / published
TUM Einrichtung:
Lehrstuhl für Mathematische Statistik
Format:
Text
 BibTeX