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On the 1/H-variation of the divergence integral with respect to a Hermite process

Author

Listed:
  • Čoupek, Petr
  • Kříž, Pavel
  • Svoboda, Matěj

Abstract

In this paper, a divergence-type integral of a random integrand with respect to the Hermite process of order k∈N with Hurst parameter H ∈ (1/2, 1) is defined and it is shown that the integral is of finite 1/H-variation.

Suggested Citation

  • Čoupek, Petr & Kříž, Pavel & Svoboda, Matěj, 2026. "On the 1/H-variation of the divergence integral with respect to a Hermite process," Stochastic Processes and their Applications, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:spapps:v:195:y:2026:i:c:s0304414926000232
    DOI: 10.1016/j.spa.2026.104891
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    References listed on IDEAS

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    1. Pipiras, Vladas & Taqqu, Murad S., 2010. "Regularization and integral representations of Hermite processes," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 2014-2023, December.
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    5. Essaky, El Hassan & Nualart, David, 2015. "On the 1H-variation of the divergence integral with respect to fractional Brownian motion with Hurst parameter H<12," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4117-4141.
    6. Čoupek, Petr & Duncan, Tyrone E. & Pasik-Duncan, Bozenna, 2022. "A stochastic calculus for Rosenblatt processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 853-885.
    7. Guerra, João M.E. & Nualart, David, 2005. "The 1/H-variation of the divergence integral with respect to the fractional Brownian motion for H>1/2 and fractional Bessel processes," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 91-115, January.
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