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Fractional diffusion Bessel processes with Hurst index H∈(0,12)

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  • Mishura, Yuliya
  • Ralchenko, Kostiantyn

Abstract

We introduce fractional diffusion Bessel process with Hurst index H∈(0,12), derive a stochastic differential equation for it, and study the asymptotic properties of its sample paths.

Suggested Citation

  • Mishura, Yuliya & Ralchenko, Kostiantyn, 2024. "Fractional diffusion Bessel processes with Hurst index H∈(0,12)," Statistics & Probability Letters, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:stapro:v:206:y:2024:i:c:s0167715223002328
    DOI: 10.1016/j.spl.2023.110008
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    References listed on IDEAS

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    1. Hu, Yaozhong & Nualart, David & Song, Xiaoming, 2008. "A singular stochastic differential equation driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2075-2085, October.
    2. Xichao Sun & Rui Guo & Ming Li, 2020. "Some Properties of Bifractional Bessel Processes Driven by Bifractional Brownian Motion," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-13, October.
    3. Y. Hu & D. Nualart, 2005. "Some Processes Associated with Fractional Bessel Processes," Journal of Theoretical Probability, Springer, vol. 18(2), pages 377-397, April.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

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