Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

Superior and Inferior Limits on the Increments of Gaussian Processes

  • Park, Yong-Kab (Department of Mathematics, Gyeongsang National University, Chinju, 660-701) ;
  • Hwang, Kyo-Shin (Department of Mathematics, Gyeongsang National University, Chinju, 660-701) ;
  • Park, Soon-Kyu (Department of Computer Science, Chinju National University, Chinju, 660-150)
  • Published : 1997.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

Csorgo-Revesz type theorems for Wiener process are developed to those for Gaussian process. In particular, some results of superior and inferior limits for the increments of a Gaussian process are differently obtained under mild conditions, via estimating probability inequalities on the suprema of a Gaussian process.

Keywords

References

  1. Annals of Mathematical Statistics v.35 Limit theorems for the maximum term in stationary sequences Berman, S.M.
  2. Zeitschrift fuer Wahrscheinlichkeitsthorie und verwandte Gebiete v.46 On large intervals in the Csorgo-Revesz theorem on increments of a Wiener process Book, S.A.;Shore, T.R.
  3. Journal of Mathematics of Kyoto University v.31 no.1 Erdos-Renyi laws applied to Gaussian processes. Doct. Diss. Choi, Y.K.
  4. Stochastic Processes and Their Applications v.39 On infinite series of independent Ornstein-Uhlenbeck processes Csaki, E.;Csorgo,M.;Lin, Z.Y.;Revesz, P.
  5. Strong Approximations in Probability and Statistics Csorgo, M.;Revesz, P.
  6. Technical Report A note on increments of a Wiener process Deo, C.M.
  7. Journal of Analyse Mathematics v.23 On a New law of large numbers Erdos, P.;Renyi, A.
  8. Probability in Banach spaces, Obercalbach, Lecture Notes in Math. v.526 Evaluations of Processus Gaussiens cpmposes Fernique, X.
  9. Chinese Journal of applied Probability Statistics v.2 no.1 Some results on increments of Gaussian processes Lu, C.R.
  10. Stochastic Processes and their Applications v.18 On the Size of the increments of nonstationary Gaussian processes Ortega, J.
  11. The Bell System Technical Journal v.41 The one-sided barrier problem for Gaussian noise Slepian, D.
  12. Zeitschrift fuer Wahrscheinlichkeitstheorie und verwandte Gebiete v.3 An invariance principle for the law of iterated logarithm Strassen, V.