User: Guest  Login
Title:

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

Document type:
Zeitschriftenaufsatz
Author(s):
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.
Keywords:
Maximum increment of a random walk, dependent jump sizes; moving average process; GARCH process; stochastic volatility model; regular variation, extreme value distribution
Journal title:
Probability Theory and Related Fields
Year:
2013
Journal volume:
156
Journal issue:
1-2
Pages contribution:
249-272
Reviewed:
ja
Language:
en
Fulltext / DOI:
doi:10.1007/s00440-012-0427-2
Status:
Verlagsversion / published
TUM Institution:
Lehrstuhl für Mathematische Statistik
Format:
Text
 BibTeX