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- 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
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