The limit distribution of the maximum increment of a random walk with dependent regularly varying jump sizes
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.
Maximum increment of a random walk, dependent jump sizes; moving average process; GARCH process; stochastic volatility model; regular variation, extreme value distribution