IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v73y1998i1p1-45.html
   My bibliography  Save this article

Fractional step method for stochastic evolution equations

Author

Listed:
  • Goncharuk, Nataliya Yu.
  • Kotelenez, Peter

Abstract

This paper deals with the fractional step method in the analysis of stochastic partial differential equations (SPDEs) and their generalizations. Three types of problems are investigated. The first one is the study of invariant sets for the solution of the stochastic equations. The second one is existence of solutions for certain stochastic partial differential equations describing the mass distribution of a system of diffusing and reacting particles; the assumptions in the traditional approaches to SPDEs are not satisfied for this SPDE. The third type of problems is the numerical one: we construct solutions of a class of quasilinear stochastic differential equations of parabolic type using the fractional step method with the decomposition into linearized "drift" and pure "diffusion" equations.

Suggested Citation

  • Goncharuk, Nataliya Yu. & Kotelenez, Peter, 1998. "Fractional step method for stochastic evolution equations," Stochastic Processes and their Applications, Elsevier, vol. 73(1), pages 1-45, January.
    • Handle: RePEc:eee:spapps:v:73:y:1998:i:1:p:1-45
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(97)00079-3
    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. Dawson, D. A., 1975. "Stochastic evolution equations and related measure processes," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 1-52, March.
    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. C. Tudor & M. Tudor, 2002. "Some Properties of Solutions of Double Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 15(1), pages 129-151, January.
    2. Dorogovtsev, Andrey A. & Riabov, Georgii V. & Schmalfuß, Björn, 2020. "Stationary points in coalescing stochastic flows on R," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4910-4926.
    3. Stefan Tappe, 2022. "Invariant cones for jump-diffusions in infinite dimensions," Papers 2206.13913, arXiv.org, revised Nov 2023.

    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. Ubøe, Jan & Zhang, Tusheng, 1995. "A stability property of the stochastic heat equation," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 247-260, December.
    2. Ethier, S. N. & Krone, Stephen M., 1995. "Comparing Fleming-Viot and Dawson-Watanabe processes," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 171-190, December.
    3. Mandler, Christian & Overbeck, Ludger, 2022. "A functional Itō-formula for Dawson–Watanabe superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 202-228.
    4. Valentin Tissot-Daguette, 2023. "Occupied Processes: Going with the Flow," Papers 2311.07936, arXiv.org, revised Dec 2023.
    5. Rémillard, Bruno & Vaillancourt, Jean, 2014. "On signed measure valued solutions of stochastic evolution equations," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 101-122.
    6. Mytnik, Leonid & Neuman, Eyal, 2015. "Pathwise uniqueness for the stochastic heat equation with Hölder continuous drift and noise coefficients," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3355-3372.

    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:1-45. 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.