IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v34y1992i5p433-450.html
   My bibliography  Save this article

Explicit correction formulae for parametric identification of stochastic differential systems

Author

Listed:
  • Kazimierczyk, Piotr

Abstract

In this paper we consider the use of maximum likelihood estimators (MLEs) in the situation where the data come from a “smooth” dynamical system which is approximated by an Itô equation. It is well known that in such situation correction terms may appear already in the equation. Independently of this fact (in particular also when a correction term of a drift coefficient is vanishing) in most cases additional corrections of formulas for estimators of parameters of equation are necessary. The importance of the correction under consideration has been noticed and repeatedly indicated in several publications, but in most papers devoted to the estimation of parameters of Itô differential models it was not taken into account. The form of the correction terms seems to be known merely for linear systems. In this paper a general approach, based upon a known result of Mc Shane's, is employed to prove an appropriate convergence theorem concerning two types of integrals appearing in the formulas of MLEs and the explicit forms of correction terms are derived for nonlinear systems provided that the parameters enter the drift term linearly. The necessity of using corrections is underlined by an extremely simple example in which the neglection of correction terms leads to an infinite relative error of estimation. This theoretically established fact is also observed on the basis of numerical simulation. The second example, connected with a nonlinear stochastic oscillator, illustrates the effectiveness of estimation in presence of corrections in a practically important case (it also enlightens some earlier numerical experiences described in the literature).

Suggested Citation

  • Kazimierczyk, Piotr, 1992. "Explicit correction formulae for parametric identification of stochastic differential systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 34(5), pages 433-450.
  • Handle: RePEc:eee:matcom:v:34:y:1992:i:5:p:433-450
    DOI: 10.1016/0378-4754(92)90075-R
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037847549290075R
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/0378-4754(92)90075-R?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. Loges, Wilfried, 1984. "Girsanov's theorem in Hilbert space and an application to the statistics of Hilbert space- valued stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 17(2), pages 243-263, July.
    2. Liske, Horst & Platen, Eckhard, 1987. "Simulation studies on time discrete diffusion approximations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 29(3), pages 253-260.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kazimierczyk, Piort, 1995. "To the parametric identification of Markov diffusions; the use of the maximum quadratic variation functional," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 21-33.

    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. Yoshihiro Saito & Taketomo Mitsui, 1993. "Simulation of stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 419-432, September.
    2. Igor Cialenco, 2018. "Statistical inference for SPDEs: an overview," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 309-329, July.
    3. M. Huebner, 1999. "Asymptotic Properties of the Maximum Likelihood Estimator for Stochastic PDEs Disturbed by Small Noise," Statistical Inference for Stochastic Processes, Springer, vol. 2(1), pages 57-68, January.
    4. Kim, Yoon Tae, 1999. "Parameter estimation in infinite-dimensional stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 45(3), pages 195-204, November.
    5. Makroglou, Athena, 1992. "Collocation methods for stochastic Volterra integro-differential equations with random forcing functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 34(5), pages 459-466.

    More about this item

    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:matcom:v:34:y:1992:i:5:p:433-450. 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.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.