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Formulas for the divergence operator in isonormal Gaussian space

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  • Levental, S.
  • Vellaisamy, P.

Abstract

In this paper, we first derive some explicit formulas for the computation of the n-th order divergence operator in Malliavin calculus for the one-dimensional case. We then extend these results to the case of isonormal Gaussian space. Our results generalize some of the known results for the divergence operator. Our approach in deriving the formulas is new and simple.

Suggested Citation

  • Levental, S. & Vellaisamy, P., 2023. "Formulas for the divergence operator in isonormal Gaussian space," Statistics & Probability Letters, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:stapro:v:194:y:2023:i:c:s0167715222002565
    DOI: 10.1016/j.spl.2022.109743
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    References listed on IDEAS

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    1. Nicholas Ma & David Nualart, 2020. "Rate of Convergence for the Weighted Hermite Variations of the Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 33(4), pages 1919-1947, December.
    2. Nualart,David & Nualart,Eulalia, 2018. "Introduction to Malliavin Calculus," Cambridge Books, Cambridge University Press, number 9781107039124.
    3. Nualart,David & Nualart,Eulalia, 2018. "Introduction to Malliavin Calculus," Cambridge Books, Cambridge University Press, number 9781107611986.
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