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On superior limits for the increments of Gaussian processes

Author

Listed:
  • Kyo Shin Huang
  • Choi, Yong Kab
  • Jong Soo Jung

Abstract

Let {X(t); t [greater-or-equal, slanted] 0} be a Gaussian process with stationary increments E{X(t + s) - X(t)}2 = [sigma]2(s). Let at(t [greater-or-equal, slanted] 0) be a nondecreasing function of t with 0 [infinity] {(tk+1 - tk)/atk} [infinity] {(tk+1 - tk)/atk} [greater-or-equal, slanted] 1, then we have a value [delta] almost surely, where [delta]=inf{[gamma]>;[summation operator](tk(log(n)tk)/atk)-[gamma]2

Suggested Citation

  • Kyo Shin Huang & Choi, Yong Kab & Jong Soo Jung, 1997. "On superior limits for the increments of Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 289-296, October.
    • Handle: RePEc:eee:stapro:v:35:y:1997:i:3:p:289-296
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    References listed on IDEAS

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    1. Vasudeva, R. & Savitha, S., 1993. "On the increments of Weiner process - A look through subsequences," Stochastic Processes and their Applications, Elsevier, vol. 47(1), pages 153-158, August.
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