Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A LAW OF THE ITERATED LOGARITHM FOR lp-VALUED GAUSSIAN RANDOM FIELDS

  • Choi, Yong-Kab (DEPARTMENT OF MATHEMATICS GYEONGSANG NATIONAL UNIVERSITY) ;
  • Hwang, Kyo-Shin (DEPARTMENT OF MATHEMATICS GYEONGSANG NATIONAL UNIVERSITY) ;
  • Moon, Hee-Jin (DEPARTMENT OF MATHEMATICS GYEONGSANG NATIONAL UNIVERSITY)
  • Published : 2007.11.30
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Abstract

A general law of the iterated logarithm (LIL) is established for $l^p$-valued Gaussian random fields under explicit conditions.

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References

  1. S. M. Berman, Limit theorems for the maximum term in stationary sequence, Ann. Math. Statist. 35 (1964), 502-616 https://doi.org/10.1214/aoms/1177703551
  2. C. Borell, The Brunn-Minkowski inequality in Gauss space, Invent. Math. 30 (1975), no. 2, 205-216 https://doi.org/10.1007/BF01425510
  3. Y. K. Choi and K. S. Hwang, How big are the lag increments of a Gaussian process?, Comput. Math. Appl. 40 (2000), no. 8-9, 911-919 https://doi.org/10.1016/S0898-1221(00)85002-6
  4. E. Csaki, M. Csorgo, Z. Y. Lin, and P. Revesz, On infinite series of independent Ornstein-uhlenbeck processes, Stoch. Process. Appl. 39 (1991), no. 1, 25-44 https://doi.org/10.1016/0304-4149(91)90029-C
  5. E. Csaki, M. Csorgo, and Q. M. Shao, Fernique type Inequalities and moduli of continuity for $l^2$-valued Ornstein-Uhlenbeck Processes, Ann. Inst. H. Poincare Probab. Statist. 28 (1992), no. 4, 479-517
  6. M. Csorgo and Q. M. Shao, Strong limit theorems for large and small increments of $l^p$ -valued Gaussian Processes, Ann. Probab. 21 (1993), no. 4, 1958-1990 https://doi.org/10.1214/aop/1176989007
  7. Z. Y. Lin and Y. K. Choi, Some limit theorems for fractional Levy Brownian fields, Stoch. Process. Appl. 82 (1999), no. 2, 229-244 https://doi.org/10.1016/S0304-4149(99)00019-8
  8. Z. Y. Lin, S. H. Lee, K. S. Hwang, and Y. K. Choi, Some limit theorem on the increments of $l^p$-valued multi-parameter Gaussian processes, Acta Math. Sin. (English Ser.) 20 (2004), no. 6, 1019-1028 https://doi.org/10.1007/s10114-004-0414-3
  9. Z. Y. Lin and C. R. Lu, Strong Limit Theorems, Kluwer Academic Publ., Hong Kong, 1992
  10. L. X. Zhang, A note on liminfs for increments of a fractional Brownian motion, Acta Math. Hungar. 76 (1997), no. 1-2, 145-154 https://doi.org/10.1007/BF02907058