Free Access
Issue
ESAIM: PS
Volume 7, March 2003
Page(s) 23 - 88
DOI https://doi.org/10.1051/ps:2003008
Published online 15 May 2003
  1. O.E. Barndorff-Nielsen, Superposition of Ornstein-Uhlenbeck type processes, Technical Report 1999-2, MaPhySto. Aarhus University (1999), URL: http://www.maphysto.dk/cgi-bin/w3-msql/publications/.
  2. J. Beran, Statistics for Long-Memory Processes. Chapman & Hall, Monogr. Statist. Appl. Probab. 61 (1994).
  3. D.R. Brillinger, An introduction to polyspectra. Ann. Math. Statist. 36 (1965) 1351-1374. [CrossRef] [MathSciNet]
  4. L. Calvet and A. Fisher, Forecasting multifractal volatility. J. Econometrics 105 (2001) 27-58. [CrossRef] [MathSciNet]
  5. P. Carmona and L. Coutin, Fractional Brownian motion and the Markov property, Electron. Commun. Probab. 3 (1998) 95-107.
  6. P. Carmona, L. Coutin and G. Montseny, Applications of a representation of long-memory Gaussian processes. Stochastic Process. Appl. (submitted), URL: http://www.sv.cict.fr/lsp/Carmona/prepublications.html
  7. P. Clifford and G. Wei, The equivalence of the Cox process with squared radial Ornstein-Uhlenbeck intensity and the death process in a simple population model. Ann. Appl. Probab. 3 (1993) 863-873. [CrossRef] [MathSciNet]
  8. D.R. Cox, Long-range dependence, non-linearity and time irreversibility. J. Time Ser. Anal. 12 (1991) 329-335. [CrossRef] [MathSciNet]
  9. J.C. Cox, J.E. Ingersoll and S.A. Ross, A theory of the term structure of interest rates. Econometrica 53 (1985) 385-407. [CrossRef] [MathSciNet]
  10. T. Dankel Jr., On the distribution of the integrated square of the Ornstein-Uhlenbeck process. SIAM J. Appl. Math. 51 (1991) 568-574. [CrossRef] [MathSciNet]
  11. E.B. Dynkin, Markov Processes, Vols. 1-2. Springer-Verlag, Berlin-Göttingen-Heidelberg (1965).
  12. W. Feller, Two singular diffusion problems. Ann. Math. (2) 54 (1951) 173-182. [CrossRef] [MathSciNet]
  13. C. Granger, Long-memory relationship and aggregation of dynamic models. J. Econometrics 14 (1980) 227-238. [CrossRef] [MathSciNet]
  14. R.C. Griffiths, Infinitely divisible multivariate gamma distributions. Sankhya Ser. A 32 (1970) 393-404. [MathSciNet]
  15. E. Iglói, Long-range dependent processes with real bispectrum are third order nonlinear, Technical Report 259 (2001/1). University of Debrecen, Institute of Mathematics and Informatics (2001).
  16. E. Iglói and G. Terdik, Long-range dependence through Gamma-mixed Ornstein-Uhlenbeck process. Electron. J. Probab. (EJP) 4 (1999) 1-33.
  17. N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes. North-Holland Publishing Co.,Amsterdam (1981).
  18. S. Jaffard, The multifractal nature of Lévy processes. Probab. Theory Related Fields 114 (1999) 207-227. [CrossRef] [MathSciNet]
  19. S. Karlin and J. McGregor, Classical diffusion processes and total positivity. J. Math. Anal. Appl. 1 (1960) 163-183. [CrossRef] [MathSciNet]
  20. K. Kawazu and S. Watanabe, Branching processes with immigration and related limit theorems. Teor. Verojatnost. Primenen. 16 (1971) 34-51.
  21. A.N. Kolmogorov, Über die analitischen Methoden in der Wahrscheinlichkeitsrechnung. Math. Ann. 104 (1931) 415-458. [CrossRef] [MathSciNet]
  22. A.N. Kolmogorov, Wiener spiral and some other interesting curve in Hilbert space. C. R. Acad. Sci. URSS 26 (1940) 115-118.
  23. A.N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C. R. Acad. Sci. URSS 30 (1941) 301-305.
  24. P.R. Krishnaiah and M.M. Rao, Remarks on a multivariate gamma distribution. Amer. Math. Monthly 68 (1961) 342-346. [CrossRef] [MathSciNet]
  25. A.S. Krishnamoorthy and M. Parthasarathy, A multi-variate gamma-type distribution. Ann. Math. Statist. 22 (1951) 549-557. [CrossRef]
  26. W.E. Leland, M.S. Taqqu, W. Willinger and D.W. Wilson, On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Trans. Networking 2 (1994) 1-15. [CrossRef]
  27. S.B. Lowen and M.C. Teich, Fractal renewal processes generate 1/f noise. Phys. Rev. E 47 (1993) 992-1001. [CrossRef]
  28. B.B. Mandelbrot, Long-run linearity, locally Gaussian processes, h-spectra and infinite variances. Technometrics 10 (1969) 82-113.
  29. B.B. Mandelbrot and J.W. Van Ness, Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10 (1968) 422-437. [NASA ADS] [CrossRef] [MathSciNet]
  30. A.P. Prudnikov, Y.A. Britshkov and O.I. Maritshev, Integrali i ryadi. Nauka, Moscow. Appl. Math. (1981), in Russian.
  31. H.R. Riedi, S.M. Crouse, J.V. Ribeiro and G.R. Baraniuk, A multifractal wavelet model with application to network traffic. IEEE Trans. Inform. Theory 45 (1999) 992-1018. [CrossRef] [MathSciNet]
  32. B. Ryu and S.B. Lowen, Point process models for self-similar network traffic, with applications. Comm. Statist. Stochastic Models 14 (1998) 735-761. [CrossRef] [MathSciNet]
  33. G. Samorodnitsky and M.S. Taqqu, Linear models with long-range dependence and finite or infinite variance, edited by D. Brillinger, P. Caines, J. Geweke, E. Parzen, M. Rosenblatt and M.S. Taqqu, New Directions in Time Series Analysis, Part II. Springer-Verlag, New York, IMA Vol. Math. Appl. 46 (1992) 325-340.
  34. T. Shiga and S. Watanabe, Bessel diffusions as a one-parameter family of diffusion processes. Z. Wahrsch. Verw. Gebiete 27 (1973) 37-46. [CrossRef]
  35. A.N. Shiryaev, Probability. Springer-Verlag, New York (1996).
  36. S.E. Shreve, Steven shreve's lectures on stochastic calculus and finance, Online: www.cs.cmu.edu/chal/shreve.html
  37. Y.G. Sinai, Self-similar probability distributions. Theor. Probab. Appl. 21 (1976) 64-84. [CrossRef]
  38. G. Szego, Orthogonal polynomials, in Colloquium Publ., Vol. XXIII. American Math. Soc., New York (1936).
  39. M.S. Taqqu, V. Teverovsky and W. Willinger, Is network traffic self-similar or multifractal? Fractals 5 (1997) 63-73.
  40. G. Terdik, Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis; A Frequency Domain Approach. Springer-Verlag, New York, Lecture Notes in Statist. 142 (1999).
  41. G. Terdik, Z. Gál, S. Molnár and E. Iglói, Bispectral analysis of traffic in high speed networks. Comput. Math. Appl. 43 (2002) 1575-1583. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  42. W. Willinger, M.S. Taqqu, R. Sherman and D.V. Wilson, Self-similarity through high variability: Statistical analysis of Ethernet LAN traffic at the source level. Comput. Commun. Rev. 25 (1995) 100-113. [CrossRef]
  43. T. Yamada and S. Watanabe, On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11 (1971) 155-167. [MathSciNet]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.