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


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 


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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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