, Volume 16, Issue 2, pp 241–254 | Cite as

Limit theorems for extremes of strongly dependent cyclo-stationary χ-processes

  • Zhongquan Tan
  • Enkelejd Hashorva


In this paper, with motivation from the paper of Konstant et al. (Lith Math J 44:196-208, 2004) we derive limit theorems for the maximum of strongly dependent cyclo-stationary \(\chi \)-processes. Further, under a global Hölder condition we show that Seleznjev pth-mean convergence theorem holds.


Gaussian process Cyclo-stationary process \(\chi\)-process Gumbel limit law Limit theorem Seleznjev pth-mean convergence theorem Piterbarg inequality 

AMS 2000 Subject Classifications

Primary—60F05; Secondary—60G15 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.College of Mathematics, Physics and Information EngineeringJiaxing UniversityJiaxingPeople’s Republic of China
  2. 2.Department of Actuarial Science, Faculty of Business and EconomicsUniversity of LausanneLausanneSwitzerland

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