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Convergence in Law to Operator Fractional Brownian Motions

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  • Hongshuai Dai

    (Guangxi University)

Abstract

In this paper, we provide two approximations in law of operator fractional Brownian motions. One is constructed by Poisson processes, and the other generalizes a result of Taqqu (Z. Wahrscheinlichkeitstheor. Verw. Geb. 31:287–302, 1975).

Suggested Citation

  • Hongshuai Dai, 2013. "Convergence in Law to Operator Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 26(3), pages 676-696, September.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:3:d:10.1007_s10959-011-0401-4
    DOI: 10.1007/s10959-011-0401-4
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    References listed on IDEAS

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    1. Delgado, Rosario, 2007. "A reflected fBm limit for fluid models with ON/OFF sources under heavy traffic," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 188-201, February.
    2. Enriquez, Nathanaël, 2004. "A simple construction of the fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 203-223, February.
    3. Maejima, Makoto & Mason, J. David, 1994. "Operator-self-similar stable processes," Stochastic Processes and their Applications, Elsevier, vol. 54(1), pages 139-163, November.
    4. Juan J. Dolado & Francesc Marmol, 2004. "Asymptotic inference results for multivariate long-memory processes," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 168-190, June.
    5. Dai, Hongshuai & Li, Yuqiang, 2010. "A weak limit theorem for generalized multifractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 348-356, March.
    6. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(5), pages 621-642, October.
    7. Davidson, James & Hashimzade, Nigar, 2008. "Alternative Frequency And Time Domain Versions Of Fractional Brownian Motion," Econometric Theory, Cambridge University Press, vol. 24(1), pages 256-293, February.
    8. Chung, Ching-Fan, 2002. "Sample Means, Sample Autocovariances, And Linear Regression Of Stationary Multivariate Long Memory Processes," Econometric Theory, Cambridge University Press, vol. 18(1), pages 51-78, February.
    9. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
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    Cited by:

    1. Hongshuai Dai, 2022. "Tandem fluid queue with long-range dependent inputs: sticky behaviour and heavy traffic approximation," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 165-196, June.

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