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Approximation to two independent Gaussian processes from a unique Lévy process and applications

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  • Jun Wang
  • Xianmei Song
  • Guangjun Shen
  • Xiuwei Yin

Abstract

In this article, we construct two families of processes, from a unique Lévy process, the finite dimensional distributions of which converge in law towards the finite dimensional distributions of the two independent Gaussian processes. As applications of this result, we obtain families of processes that converge in law towards fractional Brownian motion, sub-fractional Brownian motion and bifractional Brownian motion, respectively.

Suggested Citation

  • Jun Wang & Xianmei Song & Guangjun Shen & Xiuwei Yin, 2020. "Approximation to two independent Gaussian processes from a unique Lévy process and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(21), pages 5220-5234, November.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:21:p:5220-5234
    DOI: 10.1080/03610926.2019.1615095
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