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The law of the iterated logarithm for functionals of the Wiener process

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  • Logachov, A.
  • Yambartsev, A.

Abstract

In this note, we establish a law of the iterated logarithm for Fréchet differentiable functionals of a general form with respect to the Wiener process for a small time. The proof method shares conceptual similarities with the delta method.

Suggested Citation

  • Logachov, A. & Yambartsev, A., 2025. "The law of the iterated logarithm for functionals of the Wiener process," Statistics & Probability Letters, Elsevier, vol. 219(C).
    • Handle: RePEc:eee:stapro:v:219:y:2025:i:c:s0167715224003109
    DOI: 10.1016/j.spl.2024.110341
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    References listed on IDEAS

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    1. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, January.
    2. Prakash Gorroochurn, 2020. "Who Invented the Delta Method, Really?," The Mathematical Intelligencer, Springer, vol. 42(3), pages 46-49, September.
    3. Anil K. Bera & Malabika Koley, 2023. "A History of the Delta Method and Some New Results," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 272-306, November.
    Full references (including those not matched with items on IDEAS)

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