IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v182y2025ics0304414925000171.html

Almost sure approximations and laws of iterated logarithm for signatures

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414925000171
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2025.104576?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Kanagawa, S. & Yoshihara, K., 1994. "The almost sure invariance principles of degenerate U-statistics of degree two for stationary random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(2), pages 347-356, February.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kifer, Yuri, 2013. "Strong approximations for nonconventional sums and almost sure limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2286-2302.
    2. Pelletier, Mariane, 1999. "An Almost Sure Central Limit Theorem for Stochastic Approximation Algorithms," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 76-93, October.
    3. Gao, Fuqing & Jiang, Hui, 2010. "Large deviations for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2212-2240, November.
    4. Luísa Pereira & Zhongquan Tan, 2017. "Almost Sure Convergence for the Maximum of Nonstationary Random Fields," Journal of Theoretical Probability, Springer, vol. 30(3), pages 996-1013, September.
    5. Mikhail Gordin & Michel Weber, 2002. "On the Almost Sure Central Limit Theorem for a Class of Z d -Actions," Journal of Theoretical Probability, Springer, vol. 15(2), pages 477-501, April.
    6. Aleksandar Arandjelović & Thorsten Rheinländer & Pavel V. Shevchenko, 2025. "Importance sampling for option pricing with feedforward neural networks," Finance and Stochastics, Springer, vol. 29(1), pages 97-141, January.
    7. Hu, Zhishui & Wang, Wei & Dong, Liang, 2025. "Strong approximations in the almost sure central limit theorem and limit behavior of the center of mass," Stochastic Processes and their Applications, Elsevier, vol. 182(C).
    8. Denker, Manfred & Zheng, Xiaofei, 2018. "On the local times of stationary processes with conditional local limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2448-2462.
    9. Li, Miaomiao & Li, Yunzhang & Pei, Bin & Xu, Yong, 2025. "Averaging principle for semilinear slow–fast rough partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 188(C).
    10. Shigeki Aida, 2024. "Rough Differential Equations Containing Path-Dependent Bounded Variation Terms," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2130-2183, September.
    11. Ibragimov, Ildar & Lifshits, Mikhail, 1998. "On the convergence of generalized moments in almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 343-351, November.
    12. Bercu, B., 2004. "On the convergence of moments in the almost sure central limit theorem for martingales with statistical applications," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 157-173, May.
    13. Gautier, Eric, 2005. "Uniform large deviations for the nonlinear Schrodinger equation with multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 115(12), pages 1904-1927, December.
    14. Bardina, X. & Nourdin, I. & Rovira, C. & Tindel, S., 2010. "Weak approximation of a fractional SDE," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 39-65, January.
    15. Li, Jingyu & Zhang, Yong, 2021. "An almost sure central limit theorem for the stochastic heat equation," Statistics & Probability Letters, Elsevier, vol. 177(C).
    16. Lifshits, M. A. & Stankevich, E. S., 2001. "On the large deviation principle for the almost sure CLT," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 263-267, February.
    17. Hu, Yi-Jun, 1997. "A large deviation principle for small perturbations of random evolution equations in Hölder norm," Stochastic Processes and their Applications, Elsevier, vol. 68(1), pages 83-99, May.
    18. Heck, Matthias K., 1998. "The principle of large deviations for the almost everywhere central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 61-75, August.
    19. Holzmann, Hajo & Koch, Susanne & Min, Aleksey, 2004. "Almost sure limit theorems for U-statistics," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 261-269, September.
    20. Deuschel, Jean-Dominique & Friz, Peter K. & Maurelli, Mario & Slowik, Martin, 2018. "The enhanced Sanov theorem and propagation of chaos," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2228-2269.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:182:y:2025:i:c:s0304414925000171. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.