EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 7 (March 2003) ESAIM: PS, 7 (2003) 23-88 References
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/. [Google Scholar]
  2. J. Beran, Statistics for Long-Memory Processes. Chapman & Hall, Monogr. Statist. Appl. Probab. 61 (1994). [Google Scholar]
  3. D.R. Brillinger, An introduction to polyspectra. Ann. Math. Statist. 36 (1965) 1351-1374. [Google Scholar]
  4. L. Calvet and A. Fisher, Forecasting multifractal volatility. J. Econometrics 105 (2001) 27-58. [Google Scholar]
  5. P. Carmona and L. Coutin, Fractional Brownian motion and the Markov property, Electron. Commun. Probab. 3 (1998) 95-107. [Google Scholar]
  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 [Google Scholar]
  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] [Google Scholar]
  8. D.R. Cox, Long-range dependence, non-linearity and time irreversibility. J. Time Ser. Anal. 12 (1991) 329-335. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  11. E.B. Dynkin, Markov Processes, Vols. 1-2. Springer-Verlag, Berlin-Göttingen-Heidelberg (1965). [Google Scholar]
  12. W. Feller, Two singular diffusion problems. Ann. Math. (2) 54 (1951) 173-182. [Google Scholar]
  13. C. Granger, Long-memory relationship and aggregation of dynamic models. J. Econometrics 14 (1980) 227-238. [CrossRef] [MathSciNet] [Google Scholar]
  14. R.C. Griffiths, Infinitely divisible multivariate gamma distributions. Sankhya Ser. A 32 (1970) 393-404. [MathSciNet] [Google Scholar]
  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). [Google Scholar]
  16. E. Iglói and G. Terdik, Long-range dependence through Gamma-mixed Ornstein-Uhlenbeck process. Electron. J. Probab. (EJP) 4 (1999) 1-33. [Google Scholar]
  17. N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes. North-Holland Publishing Co.,Amsterdam (1981). [Google Scholar]
  18. S. Jaffard, The multifractal nature of Lévy processes. Probab. Theory Related Fields 114 (1999) 207-227. [CrossRef] [MathSciNet] [Google Scholar]
  19. S. Karlin and J. McGregor, Classical diffusion processes and total positivity. J. Math. Anal. Appl. 1 (1960) 163-183. [CrossRef] [MathSciNet] [Google Scholar]
  20. K. Kawazu and S. Watanabe, Branching processes with immigration and related limit theorems. Teor. Verojatnost. Primenen. 16 (1971) 34-51. [Google Scholar]
  21. A.N. Kolmogorov, Über die analitischen Methoden in der Wahrscheinlichkeitsrechnung. Math. Ann. 104 (1931) 415-458. [CrossRef] [MathSciNet] [Google Scholar]
  22. A.N. Kolmogorov, Wiener spiral and some other interesting curve in Hilbert space. C. R. Acad. Sci. URSS 26 (1940) 115-118. [Google Scholar]
  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. [Google Scholar]
  24. P.R. Krishnaiah and M.M. Rao, Remarks on a multivariate gamma distribution. Amer. Math. Monthly 68 (1961) 342-346. [CrossRef] [MathSciNet] [Google Scholar]
  25. A.S. Krishnamoorthy and M. Parthasarathy, A multi-variate gamma-type distribution. Ann. Math. Statist. 22 (1951) 549-557. [CrossRef] [Google Scholar]
  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. [Google Scholar]
  27. S.B. Lowen and M.C. Teich, Fractal renewal processes generate 1/f noise. Phys. Rev. E 47 (1993) 992-1001. [CrossRef] [Google Scholar]
  28. B.B. Mandelbrot, Long-run linearity, locally Gaussian processes, h-spectra and infinite variances. Technometrics 10 (1969) 82-113. [Google Scholar]
  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] [Google Scholar]
  30. A.P. Prudnikov, Y.A. Britshkov and O.I. Maritshev, Integrali i ryadi. Nauka, Moscow. Appl. Math. (1981), in Russian. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  35. A.N. Shiryaev, Probability. Springer-Verlag, New York (1996). [Google Scholar]
  36. S.E. Shreve, Steven shreve's lectures on stochastic calculus and finance, Online: www.cs.cmu.edu/chal/shreve.html [Google Scholar]
  37. Y.G. Sinai, Self-similar probability distributions. Theor. Probab. Appl. 21 (1976) 64-84. [CrossRef] [Google Scholar]
  38. G. Szego, Orthogonal polynomials, in Colloquium Publ., Vol. XXIII. American Math. Soc., New York (1936). [Google Scholar]
  39. M.S. Taqqu, V. Teverovsky and W. Willinger, Is network traffic self-similar or multifractal? Fractals 5 (1997) 63-73. [Google Scholar]
  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). [Google Scholar]
  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. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  43. T. Yamada and S. Watanabe, On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11 (1971) 155-167. [MathSciNet] [Google Scholar]

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.