Probability Theory and Related Fields

, Volume 101, Issue 2, pp 173–192

Small values of Gaussian processes and functional laws of the iterated logarithm

  • Ditlev Monrad
  • Holger Rootzén

DOI: 10.1007/BF01375823

Cite this article as:
Monrad, D. & Rootzén, H. Probab. Th. Rel. Fields (1995) 101: 173. doi:10.1007/BF01375823


We estimate small ball probabilities for locally nondeterministic Gaussian processes with stationary increments, a class of processes that includes the fractional Brownian motions. These estimates are used to prove Chung type laws of the iterated logarithm.

Mathematics Subject Classification (1991)

60F15 60G15 60G17 60G18 

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Ditlev Monrad
    • 1
    • 3
  • Holger Rootzén
    • 2
    • 3
  1. 1.Department of StatisticsUniversity of IllinoisChampaignUSA
  2. 2.Department of MathematicsChalmers UniversityGoteborgSweden
  3. 3.Center for Stochastic ProcessesUniversity of North Carolina at Chapel HillChapel HillUSA

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