IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v73y1998i1p47-68.html
   My bibliography  Save this article

Product of two multiple stochastic integrals with respect to a normal martingale

Author

Listed:
  • Russo, Francesco
  • Vallois, Pierre

Abstract

Let M be a normal martingale (i.e. (t) = t), we decompose the product of two multiple stochastic integrals (with respect to M) In(f)Im(g) as a sum of n [logical and] m terms Hk. Hk is equal to the integral over k+ of the function t --> In+m-2k(hk(t,.)), with respect to the k-tensor product of d[M,M]., hk being an explicit function depending only on f and g. Our formula generalizes the well-known result concerning Brownian motion and compensated Poisson process and allows us to improve some results of Emery related to the chaos representation property of solution of the structure equation.

Suggested Citation

  • Russo, Francesco & Vallois, Pierre, 1998. "Product of two multiple stochastic integrals with respect to a normal martingale," Stochastic Processes and their Applications, Elsevier, vol. 73(1), pages 47-68, January.
    • Handle: RePEc:eee:spapps:v:73:y:1998:i:1:p:47-68
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00101-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Vallois, P., 1995. "Decomposing the Brownian path via the range process," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 211-226, February.
    2. Russo, Francesco & Vallois, Pierre, 1995. "The generalized covariation process and Ito formula," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 81-104, 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. Almada Monter, Sergio Angel, 2015. "Quadratic covariation estimates in non-smooth stochastic calculus," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 343-361.
    2. Bouchard, Bruno & Loeper, Grégoire & Tan, Xiaolu, 2022. "A ℂ0,1-functional Itô’s formula and its applications in mathematical finance," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 299-323.
    3. Etienne Tanré & Pierre Vallois, 2006. "Range of Brownian Motion with Drift," Journal of Theoretical Probability, Springer, vol. 19(1), pages 45-69, January.
    4. Blandine, Bérard Bergery & Pierre, Vallois, 2008. "Approximation via regularization of the local time of semimartingales and Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 118(11), pages 2058-2070, November.
    5. Errami, Mohammed & Russo, Francesco, 2003. "n-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes," Stochastic Processes and their Applications, Elsevier, vol. 104(2), pages 259-299, April.
    6. Bandini, Elena & Russo, Francesco, 2017. "Weak Dirichlet processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 4139-4189.
    7. Gozzi, Fausto & Russo, Francesco, 2006. "Weak Dirichlet processes with a stochastic control perspective," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1563-1583, November.
    8. Bernt {O}ksendal & Elin R{o}se, 2015. "A white noise approach to insider trading," Papers 1508.06376, arXiv.org.
    9. Čoupek, Petr & Duncan, Tyrone E. & Pasik-Duncan, Bozenna, 2022. "A stochastic calculus for Rosenblatt processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 853-885.

    More about this item

    Keywords

    60G44 60H05 60H07 60J65;

    JEL classification:

    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:73:y:1998:i:1:p:47-68. 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.