IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v23y2010i3d10.1007_s10959-010-0287-6.html
   My bibliography  Save this article

A Stochastic Taylor-Like Expansion in the Rough Path Theory

Author

Listed:
  • Yuzuru Inahama

    (Nagoya University)

Abstract

In this paper, we establish a Taylor-like expansion in the context of rough path theory for a family of Itô maps indexed by a small parameter. We treat not only the case that the roughness p satisfies [p]=2, but also the case that [p]≥3. As an application, we discuss the Laplace asymptotics for Itô functionals of Brownian rough paths.

Suggested Citation

  • Yuzuru Inahama, 2010. "A Stochastic Taylor-Like Expansion in the Rough Path Theory," Journal of Theoretical Probability, Springer, vol. 23(3), pages 671-714, September.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:3:d:10.1007_s10959-010-0287-6
    DOI: 10.1007/s10959-010-0287-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-010-0287-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-010-0287-6?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Baudoin, Fabrice & Coutin, Laure, 2007. "Operators associated with a stochastic differential equation driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 117(5), pages 550-574, May.
    2. 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.
    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. 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.
    2. Sreekar Vadlamani, 2010. "Fractional Brownian Flows," Journal of Theoretical Probability, Springer, vol. 23(1), pages 257-276, March.
    3. Hufei Li & Shaojuan Ma, 2023. "The Evolution of Probability Density Function for Power System Excited by Fractional Gaussian Noise," Mathematics, MDPI, vol. 11(13), pages 1-16, June.
    4. 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.
    5. Qi Feng & Jianfeng Zhang, 2021. "Cubature Method for Stochastic Volterra Integral Equations," Papers 2110.12853, arXiv.org, revised Jul 2023.
    6. 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.
    7. Cont, Rama & Kalinin, Alexander, 2020. "On the support of solutions to stochastic differential equations with path-dependent coefficients," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2639-2674.
    8. Yaozhong Hu & Samy Tindel, 2013. "Smooth Density for Some Nilpotent Rough Differential Equations," Journal of Theoretical Probability, Springer, vol. 26(3), pages 722-749, September.
    9. Peter Kloeden & Andreas Neuenkirch & Raffaella Pavani, 2011. "Multilevel Monte Carlo for stochastic differential equations with additive fractional noise," Annals of Operations Research, Springer, vol. 189(1), pages 255-276, September.
    10. Neuenkirch, A. & Tindel, S. & Unterberger, J., 2010. "Discretizing the fractional Lévy area," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 223-254, February.
    11. Baudoin, Fabrice & Ouyang, Cheng, 2011. "Small-time kernel expansion for solutions of stochastic differential equations driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 759-792, April.
    12. Alexandra Chronopoulou & Samy Tindel, 2013. "On inference for fractional differential equations," Statistical Inference for Stochastic Processes, Springer, vol. 16(1), pages 29-61, April.
    13. Song, Jian & Tindel, Samy, 2022. "Skorohod and Stratonovich integrals for controlled processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 569-595.
    14. Passeggeri, Riccardo, 2020. "On the signature and cubature of the fractional Brownian motion for H>12," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1226-1257.

    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:spr:jotpro:v:23:y:2010:i:3:d:10.1007_s10959-010-0287-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.