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Volumn 35, Issue 2, 2007, Pages 528-550

Scaling limits for random fields with long-range dependence

Author keywords

Fractional Brownian motion; Fractional Gaussian noise; Long range dependence; Riesz energy; Self similar random field; Stable random measure

Indexed keywords


EID: 51149083477     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117906000000700     Document Type: Article
Times cited : (43)

References (15)
  • 1
    • 51149122725 scopus 로고    scopus 로고
    • BINGHAM, N. H., GOLDIE, C. M. and TEUGELS, J. L. (1987). Regular Variation. Cambridge Univ. Press. MR0898871
    • BINGHAM, N. H., GOLDIE, C. M. and TEUGELS, J. L. (1987). Regular Variation. Cambridge Univ. Press. MR0898871
  • 2
    • 4944232493 scopus 로고    scopus 로고
    • Convergence of scaled renewal processes and a packet arrival model
    • MR1996275
    • GAIGALAS, R. and KAJ, I. (2003). Convergence of scaled renewal processes and a packet arrival model. Bernoulli 9 671-703. MR1996275
    • (2003) Bernoulli , vol.9 , pp. 671-703
    • GAIGALAS, R.1    KAJ, I.2
  • 3
    • 0030502739 scopus 로고    scopus 로고
    • On the prediction of fractional Brownian motion
    • MR1385349
    • GRIPENBERG, G. and NORROS, I. (1996). On the prediction of fractional Brownian motion. J. Appl. Probab. 33 400-410. MR1385349
    • (1996) J. Appl. Probab , vol.33 , pp. 400-410
    • GRIPENBERG, G.1    NORROS, I.2
  • 4
    • 31344433287 scopus 로고    scopus 로고
    • Limiting fractal random processes in heavy-tailed systems
    • J. Lévy-Léhel and E. Lutton, eds, Springer, London
    • KAJ, I. (2005). Limiting fractal random processes in heavy-tailed systems. In Fractals in Engineering, New Trends in Theory and Applications (J. Lévy-Léhel and E. Lutton, eds.) 199-218. Springer, London.
    • (2005) Fractals in Engineering, New Trends in Theory and Applications , pp. 199-218
    • KAJ, I.1
  • 6
    • 51149112992 scopus 로고    scopus 로고
    • KAJ, I. and TAQQU, M. S. (2004). Convergence to fractional Brownian motion and to the Telecom process: The integral representation approach. Preprint, Dept. Mathematics, Uppsala Univ.
    • KAJ, I. and TAQQU, M. S. (2004). Convergence to fractional Brownian motion and to the Telecom process: The integral representation approach. Preprint, Dept. Mathematics, Uppsala Univ.
  • 7
    • 51149105195 scopus 로고    scopus 로고
    • KALLENBERG, O. (2002). Foundations of Modern Probability, 2nd. ed. Springer, New York. MR1876169
    • KALLENBERG, O. (2002). Foundations of Modern Probability, 2nd. ed. Springer, New York. MR1876169
  • 8
    • 0032382395 scopus 로고    scopus 로고
    • KONSTANTOPOULOS, T. and LIN, S.-J. (1998). Macroscopic models for long-range dependent network traffic. Queueing Syst. 28 215-243. MRI628422
    • KONSTANTOPOULOS, T. and LIN, S.-J. (1998). Macroscopic models for long-range dependent network traffic. Queueing Syst. 28 215-243. MRI628422
  • 9
    • 0001325574 scopus 로고    scopus 로고
    • Limit theorems for workload input models
    • F. P. Kelly, S. Zachary and I. Ziedins, eds, Oxford Univ. Press
    • KURTZ, T. G. (1996). Limit theorems for workload input models. In Stochastic Networks: Theory and Applications (F. P. Kelly, S. Zachary and I. Ziedins, eds.) 119-139. Oxford Univ. Press.
    • (1996) Stochastic Networks: Theory and Applications , pp. 119-139
    • KURTZ, T.G.1
  • 10
    • 51149085549 scopus 로고    scopus 로고
    • LANDKOF, N. S. (1972). Foundations of Modern Potential Theory. Springer, New York. MR0350027
    • LANDKOF, N. S. (1972). Foundations of Modern Potential Theory. Springer, New York. MR0350027
  • 11
    • 0000501589 scopus 로고
    • Fractional Brownian motions, fractional noises and applications
    • MR0242239
    • MANDELBROT, B. B. and VAN NESS, J. W. (1968). Fractional Brownian motions, fractional noises and applications. SIAMRev. 10 422-437. MR0242239
    • (1968) SIAMRev , vol.10 , pp. 422-437
    • MANDELBROT, B.B.1    VAN NESS, J.W.2
  • 12
    • 0036114594 scopus 로고    scopus 로고
    • Is network traffic approximated by stable Lévy motion or fractional Brownian motion?
    • MR1890056
    • MIKOSCH, T., RESNICK, S. I., ROOTZÉN, H. and STEGEMAN, A. (2002). Is network traffic approximated by stable Lévy motion or fractional Brownian motion? Ann. Appl. Probab. 12 23-68. MR1890056
    • (2002) Ann. Appl. Probab , vol.12 , pp. 23-68
    • MIKOSCH, T.1    RESNICK, S.I.2    ROOTZÉN, H.3    STEGEMAN, A.4
  • 13
    • 51149107128 scopus 로고    scopus 로고
    • RUDIN, W. (1987). Real and Complex Analysis, 3rd ed. McGraw-Hill, New York. MR0924157
    • RUDIN, W. (1987). Real and Complex Analysis, 3rd ed. McGraw-Hill, New York. MR0924157
  • 14
    • 51149099497 scopus 로고    scopus 로고
    • SAMORODNITSKY, G. and TAQQU, M. S. (1994). Stable Non-Gaussian Random Processes: Stochastics Models with Infinite Variance. Chapman and Hall, London. MR1280932
    • SAMORODNITSKY, G. and TAQQU, M. S. (1994). Stable Non-Gaussian Random Processes: Stochastics Models with Infinite Variance. Chapman and Hall, London. MR1280932
  • 15
    • 51149108867 scopus 로고    scopus 로고
    • TAQQU, M. S. and LEVY, J. B. (1986). Using renewal processes to generate long-range dependence and high variability. In Dependence in Probability and Statistics (E. Eberlein and M. S. Taqqu, eds.) 73-89. Birkhäuser, Boston. MR0899985
    • TAQQU, M. S. and LEVY, J. B. (1986). Using renewal processes to generate long-range dependence and high variability. In Dependence in Probability and Statistics (E. Eberlein and M. S. Taqqu, eds.) 73-89. Birkhäuser, Boston. MR0899985


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.