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A first-order limit law for functionals of two independent fractional Brownian motions in the critical case

Author

Listed:
  • Junna Bi

    (East China Normal University)

  • Fangjun Xu

    (East China Normal University)

Abstract

We prove a first-order limit law for functionals of two independent $$d$$ d -dimensional fractional Brownian motions with the same Hurst index $$H=2/d\,(d\ge 4)$$ H = 2 / d ( d ≥ 4 ) , using the method of moments and extending a result by LeGall in the case of Brownian motion.

Suggested Citation

  • Junna Bi & Fangjun Xu, 2016. "A first-order limit law for functionals of two independent fractional Brownian motions in the critical case," Journal of Theoretical Probability, Springer, vol. 29(3), pages 941-957, September.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:3:d:10.1007_s10959-015-0604-1
    DOI: 10.1007/s10959-015-0604-1
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    References listed on IDEAS

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    1. David Nualart & Salvador Ortiz-Latorre, 2007. "Intersection Local Time for Two Independent Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 20(4), pages 759-767, December.
    2. Nualart, David & Xu, Fangjun, 2014. "Central limit theorem for functionals of two independent fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3782-3806.
    3. Dongsheng Wu & Yimin Xiao, 2010. "Regularity of Intersection Local Times of Fractional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 23(4), pages 972-1001, December.
    Full references (including those not matched with items on IDEAS)

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