Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON THE LARGE AND SMALL INCREMENTS OF GAUSSIAN RANDOM FIELDS

  • Zhengyan Lin (Department of Mathematics, Zhejiang University) ;
  • Park, Yong-Kab (Department of Mathematics, College of Natural Science, Gyeongsang National University)
  • Published : 2001.05.01
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Abstract

In this paper we establish limit theorems on the large and small increments of a two-parameter Gaussian random process on rectangles in the Euclidean plane via estimating upper bounds of large deviation probabilities on suprema of the two-parameter Gaussian random process.

Keywords

References

  1. J. Math. v.31 no.1 Erdos-Renyi type laws applied to Gaussian processes Y. K. Choi
  2. J. Math. v.31 no.3 On the asymptotic behavior of Gaussian sequences with stationary increments Y. K. Choi;N. Kono
  3. J. Theoret. Probab. v.12 no.1 How big are the increments of a two-parameter Gaussian Process?
  4. East Asian Math. J. v.14 no.1 A version of Fernique lemma for Gaussian processes Y. K. Choi;Z. Y. Lin
  5. Ann. Probab. v.20 no.2 Inequalities for increments of stochastic processes and moduli of continuity E. Csaki;M. Csorgo
  6. Acta Sci. Math. v.60 Moduli of continuity for lp-valued Gaussian processes E. Csaki;M. Csorgo;Q. M. Shao
  7. Stochastic Process. Appl. v.39 On infinite series of independent Ornstein-Uhlenbeck processes E. Csaki;M. Csorgo;Z. Y. Lin;P. Revesz
  8. Z. Wahrsch. verw. Gebiete v.42 How big are the increments of a multi-parameter Wiener process? M. Csorgo;P. Pevesz
  9. Ann. Probab. v.7 How big are the increments of a Wiener process?
  10. Strong Approximations in Probability and Statistics
  11. Ann. Probab. v.21 no.4 Strong limit theorems for large and small increments of lp-valued Gaussian processes M. Csorgo;Q. M. Shao
  12. Proc. Amer. Math. Soc. v.121 no.1 Path properties for l∞-valued Gaussian processes M. Csorgo;Z. Y. Lin;Q. M. Shao
  13. Canad. J. Math. v.46 no.1 Kernel generated two-time parameter Gaussian processes and some of their path properties
  14. C. R. Acad. Sci. Paris, t. v.258 Continuite des processus Gaussiens X. Fernique
  15. Probab. Theory Related Fields v.87 Upper classes for the increments of fractional Wiener process K. Grill
  16. Ann. Probab. v.11 no.4 Some more results on increments of the Wiener process D. L. Hanson;R. P. Russo
  17. Ann. Probab. v.17 no.3 Some "liminf" results for increments of a Wiener process
  18. Chinese J. Appl. Probab. Statist. v.3 Some results on the increments of a two-parameter Wiener process F. C. Kong
  19. Trends in Probability and Related Analysis, SAP'96 The exact modulus of continuity for Gaussian processes taking values of a finite dimensional normed space N. Kono
  20. Extremes and Related Properties of Random Sequences and Processes M. R. Leadbetter;G. Lindgren;H. Rootzen
  21. processus stochastiques et mouvement brownien(2nd edn) P. Levy
  22. Scientia Sinica v.28 On increments of two-parameter Wiener process Z. Y. Lin
  23. Sci. China. Ser. v.A 40 no.4 How big are the increments of lp-valued Gaussian Processes? Z. Y. Lin
  24. Strong Limit Theorems Z. Y. Lin;C. R. Lu
  25. On the size of the increments of non-stationary Gaussian processes v.18 J. Ortega
  26. Z. Wahrsch. verw. Gebiete v.65 On the increments of the Wiener process J. Ortega;M. Wschebor