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Asymptotic behavior for an additive functional of two independent self-similar Gaussian processes

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  • Nualart, David
  • Xu, Fangjun

Abstract

We derive the asymptotic behavior for an additive functional of two independent self-similar Gaussian processes when their intersection local time exists, using the method of moments.

Suggested Citation

  • Nualart, David & Xu, Fangjun, 2019. "Asymptotic behavior for an additive functional of two independent self-similar Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3981-4008.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:10:p:3981-4008
    DOI: 10.1016/j.spa.2018.11.009
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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.
    2. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2004. "Sub-fractional Brownian motion and its relation to occupation times," RePAd Working Paper Series lrsp-TRS376, Département des sciences administratives, UQO.
    3. Harnett, Daniel & Nualart, David, 2018. "Central limit theorem for functionals of a generalized self-similar Gaussian process," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 404-425.
    4. Bojdecki, Tomasz & Gorostiza, Luis G. & Talarczyk, Anna, 2004. "Sub-fractional Brownian motion and its relation to occupation times," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 405-419, October.
    5. Russo, Francesco & Tudor, Ciprian A., 2006. "On bifractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 830-856, May.
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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.

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