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Limit theorems for functionals of two independent Gaussian processes

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  • Song, Jian
  • Xu, Fangjun
  • Yu, Qian

Abstract

Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and bi-fractional Brownian motion. A new and interesting phenomenon is that, in comparison with the results for fractional Brownian motion, extra randomness appears in the limiting distributions for Gaussian processes with nonstationary increments, say sub-fractional Brownian motion and bi-fractional Brownian. The results are obtained based on the method of moments, in which Fourier analysis, the chaining argument introduced in [11] and a pairing technique are employed.

Suggested Citation

  • Song, Jian & Xu, Fangjun & Yu, Qian, 2019. "Limit theorems for functionals of two independent Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4791-4836.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:11:p:4791-4836
    DOI: 10.1016/j.spa.2018.12.014
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Qian Yu, 2021. "Higher-Order Derivative of Self-Intersection Local Time for Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 34(4), pages 1749-1774, December.
    2. Hong, Minhao & Xu, Fangjun, 2021. "Derivatives of local times for some Gaussian fields II," Statistics & Probability Letters, Elsevier, vol. 172(C).

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