User: Guest  Login
Document type:
Zeitschriftenaufsatz 
Author(s):
Mikosch, T., and Moser, M. 
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 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 
Status:
Verlagsversion / published 
TUM Institution:
Lehrstuhl für Mathematische Statistik 
Format:
Text