Handbook of Financial Time Series

pp 653-667


Extremes of Continuous–Time Processes.

  • Vicky FasenAffiliated withTechnische Universität München, Zentrum Mathematik Email author 

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In this paper we present a review on the extremal behavior of stationary continuous-time processes with emphasis on generalized Ornstein-Uhlenbeck processes. We restrict our attention to heavy-tailed models like heavy-tailed Ornstein-Uhlenbeck processes or continuous-time GARCH processes. The survey includes the tail behavior of the stationary distribution, the tail behavior of the sample maximum and the asymptotic behavior of sample maxima of our models.