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Inequalities for the norms of integrals with respect to a fractional Brownian motion

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  • Slominski, Leszek
  • Ziemkiewicz, Bartosz

Abstract

Integrals with respect to a fractional Brownian motion with Hurst index for integrands X={Xt;t[set membership, variant][0,T]} with possibly nonregular paths are considered. General inequalities for the norms of such integrals are given.

Suggested Citation

  • Slominski, Leszek & Ziemkiewicz, Bartosz, 2005. "Inequalities for the norms of integrals with respect to a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 73(1), pages 79-90, June.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:1:p:79-90
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    References listed on IDEAS

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    1. Novikov, Alexander & Valkeila, Esko, 1999. "On some maximal inequalities for fractional Brownian motions," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 47-54, August.
    2. Mémin, Jean & Mishura, Yulia & Valkeila, Esko, 2001. "Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 197-206, January.
    3. Kubilius, K., 2002. "The existence and uniqueness of the solution of an integral equation driven by a p-semimartingale of special type," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 289-315, April.
    4. Bender, Christian, 2003. "An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter," Stochastic Processes and their Applications, Elsevier, vol. 104(1), pages 81-106, March.
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    Cited by:

    1. Yaskov, Pavel, 2018. "Extensions of the sewing lemma with applications," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3940-3965.

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