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Almost sure approximations and laws of iterated logarithm for signatures

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  • Kifer, Yuri

Abstract

We obtain strong invariance principles for normalized multiple iterated sums and integrals of the form SN(ν)(t)=N−ν/2∑0≤k1<...

Suggested Citation

  • Kifer, Yuri, 2025. "Almost sure approximations and laws of iterated logarithm for signatures," Stochastic Processes and their Applications, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:spapps:v:182:y:2025:i:c:s0304414925000171
    DOI: 10.1016/j.spa.2025.104576
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    References listed on IDEAS

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    1. Ledoux, M. & Qian, Z. & Zhang, T., 2002. "Large deviations and support theorem for diffusion processes via rough paths," Stochastic Processes and their Applications, Elsevier, vol. 102(2), pages 265-283, December.
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    3. Lacey, Michael T. & Philipp, Walter, 1990. "A note on the almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 201-205, March.
    4. Baldi, P. & Ben Arous, G. & Kerkyacharian, G., 1992. "Large deviations and the Strassen theorem in Hölder norm," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 171-180, August.
    5. Wang, Jia-gang, 1993. "A law of the iterated logarithm for stochastic integrals," Stochastic Processes and their Applications, Elsevier, vol. 47(2), pages 215-228, September.
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