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We characterize the lower classes of the integrated fractional Brownian motion by an integral test.

  • [1]

    Beran, J., Statistics for Long-Mem,ory Processes, Monographs on Statistics and Applied Probability, 61, Chapman and Hall, 1994. MR 96b:62138

    • Search Google Scholar
    • Export Citation
  • [2]

    Borell, C., Convex measures on locally convex spaces, Ark. Math. 12 (1974), 239252. MR 52#9311

  • [3]

    El-Nouty, C., On the lower classes of fractional Brownian motion, Studia Sci. Math. Hunyar. 37 (2001). MR 2003d:60159

  • [4]

    El-Nouty, C., Lower classes of fractional Brownian motion under Holder norms, Limit Theorems in Probability and Statistics, Balatonlelle, 1999 (I. Berkes, E. Csâki, M. Csörgo, eds.), Jânos Bolyai Mathematical Society, Budapest, 2002.

    • Search Google Scholar
    • Export Citation
  • [5]

    Embrechts, P. and Maejima , М., Selfsimilar Processes, Princeton Series in Applied Mathematics, Princeton University Press, Princeton NJ, 2002. MR 1920153

    • Search Google Scholar
    • Export Citation
  • [6]

    Khoshnevisan, D. and Shi, Z., Chung’s law for integrated Brownian motion, Trans. Amer. Math. Soc. 350 (1998), 42534264. MR 98m:60056

    • Search Google Scholar
    • Export Citation
  • [7]

    Kuelbs, J., Li, W. V. and Shao Q. М., Small Ball Probabilities for Gaussian Processes with Stationary Increments under Holder norms, J. Theoret. Probab. 8 (1995), 361386. MR 96b:60096

    • Search Google Scholar
    • Export Citation
  • [8]

    Li, W. V. and Linde, W., Approximation, metric entropy and small ball estimates for Gaussian measures, Ann. Probab. 27 (1999), 15561578. MR 2001c:60059

    • Search Google Scholar
    • Export Citation
  • [9]

    Li, W. V. and Shao Q. М., Small Ball Estimates for Gaussian Processes under Sobolev type norms, J. Theoret. Probab. 12 (1999), 699720. MR 2001g:60087

    • Search Google Scholar
    • Export Citation
  • [10]

    Li, W. V. and Shao, Q. М., Gaussian Processes: Inequalities, Small Ball Probabilities and Applications, Stochastic Processes: Theory and Methods, Handbook of Statistics 19, 2001. MR 1861734

    • Search Google Scholar
    • Export Citation
  • [11]

    Révész, P., On the increments of the Wiener and related processes, Ann. Probab. 10 (1982), 613622. MR 83i:60048

  • [12]

    Révész, P., Random, walk in random and non-random, environments, World Scientific Publishing Co., Teaneck, NJ, 1990. MR 92c:60096

  • [13]

    Talagrand, М., Lower classes of fractional Brownian motion, J. Theoret. Probab. 9 (1996), 191213. MR 97j:60151