The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes |
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Authors: | Thomas Mikosch Martin Moser |
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Institution: | 1. Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark 2. Institute for Advanced Study & Zentrum Mathematik, Technische Universit?t München, Boltzmannstra?e 3, 85748, Garching bei München, Germany
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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. |
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