The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes
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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.
Original language | English |
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Journal | Probability Theory and Related Fields |
Volume | 156 |
Pages (from-to) | 249-272 |
ISSN | 0178-8051 |
DOIs | |
Publication status | Published - 2013 |
ID: 46001650