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A note on functional limit theorem for the increments of FBM in sup-norm

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In this paper, using large deviation results for Gaussian processes, we establish some functional limit theorems for increments of a fractional Brownian motion in the usual sup-norm via estimating large deviation probabilities for increments of a fractional Brownian motion.

Abstract

In this paper, using large deviation results for Gaussian processes, we establish some functional limit theorems for increments of a fractional Brownian motion in the usual sup-norm via estimating large deviation probabilities for increments of a fractional Brownian motion.

참고문헌 (15)

  1. P. Baldi, "Large deviations and the Strassen theorem in Holder norm", Stoch. Proc. Appl, 42, pp.170~180 (1992)
  2. C. Borel, "A note on Gauss measure which agree on small balls", Ann. Inst. Henri Poincare Sect. B, 13(3), pp.231~238 (1977)
  3. B. Chen, , Ph. D., pp.1998
  4. B. Chen, "A functional modulus of continuity for a Wiener process", Statist. Probab. Lett, 51, pp.215~223 (2001)
  5. V. Goodman, "Rates of clustering for some Gaussian self-similar processes", Probab. Theory Rel. Fields, 88, pp.47~75 (1991)
  6. J. Kuelbs, "A strong convergence theorem for Banach space valued random variables", Ann. Probab, 4, pp.744~771 (1976)
  7. J. Kuelbs, "Small ball probabilities for Gaussian processes with stationary increments under Holder norms", J. Theore. Probab, 8(2), pp.361~386 (1995)
  8. J. Kuelbs, "Lim inf results for Gaussian samples and Chung's functional LIL", Ann. Probab, 22, pp.1879~1903 (1994)
  9. D. Monrad, "Small values of Gaussian processes and functional laws of the iterated logarithm", Probab. Theory Rel. Fields, 101, pp.173~192 (1995)
  10. C. Mueller, "A unfication of Strassen's law and Levy modulus of continuity", Z. Wahrsch. verw. Gebiete, 56, pp.163~179 (1981)
  11. J. Ortega, "On the size of the increments of non-stationary Gaussian processes", Stoch. proc. Appl, 18, pp.47~56 (1984)
  12. P. Revesz, "A Generalization of Strassen's functional law of iterated logarithm", Z. Wahrsch. verw. Gebiete, 50, pp.257~264 (1979)
  13. W. Wang, "On a functional limit result for increments of a fractional Brownian motion", Acta Math. Hungar, 93(1-2), pp.153~170 (2001)
  14. Q. Wei, "Functional limit theorems for C-R increments of k-dimensional Brownian motion in Holder norm", Acta Math. Sinica, English Series, 16(4), pp.637~654 (2000)
  15. L. X. Zhang, "A note on liminfs on increments of a fractional Brownian motion", Acta Math. Hungar, 76(1-2), pp.145~154 (1997)

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