Journal of Theoretical Probability

, Volume 30, Issue 3, pp 996–1013 | Cite as

Almost Sure Convergence for the Maximum of Nonstationary Random Fields

  • Luísa Pereira
  • Zhongquan Tan


We obtain an almost sure limit theorem for the maximum of nonstationary random fields under some dependence conditions. The obtained result is applied to Gaussian random fields.


Almost sure central limit theorem Nonstationary random field Extreme value theory 

Mathematics Subject Classification (2010)

Primary 60F05 Secondary 60G70 



The authors would like to thank the referee for several corrections and important suggestions which significantly improved this paper. Pereira’s work was supported by National Foundation of Science and Technology through UID/MAT/00212/2013. Tan’s work was supported by National Science Foundation of China (No. 11501250) and Natural Science Foundation of Zhejiang Province of China (No. LQ14A010012, LY15A010019 ).


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Beira InteriorCovilhãPortugal
  2. 2.College of Mathematics, Physics and Information EngineeringJiaxing UniversityJiaxingPeople’s Republic of China

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