IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v125y2015i12p4455-4472.html
   My bibliography  Save this article

Limit theorems for symmetric random walks and probabilistic approximation of the Cauchy problem solution for Schrödinger type evolution equations

Author

Listed:
  • Ibragimov, I.A.
  • Smorodina, N.V.
  • Faddeev, M.M.

Abstract

In the present paper we discuss a possibility to construct both a probabilistic representation and a probabilistic approximation of the Cauchy problem solution for an equation ∂u∂t=σ22Δu+V(x)u, where σ is a complex parameter such that Reσ2⩾0. This equation coincides with the heat equation when Imσ2=0 and with the Schrödinger equation when σ2=iS where S is a positive number.

Suggested Citation

  • Ibragimov, I.A. & Smorodina, N.V. & Faddeev, M.M., 2015. "Limit theorems for symmetric random walks and probabilistic approximation of the Cauchy problem solution for Schrödinger type evolution equations," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4455-4472.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:12:p:4455-4472
    DOI: 10.1016/j.spa.2015.07.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414915001623
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2015.07.005?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. Lachal, Aimé, 2008. "First hitting time and place for pseudo-processes driven by the equation subject to a linear drift," Stochastic Processes and their Applications, Elsevier, vol. 118(1), pages 1-27, January.
    2. Beghin, L. & Orsingher, E., 2005. "The distribution of the local time for "pseudoprocesses" and its connection with fractional diffusion equations," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 1017-1040, June.
    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. Marchione, Manfred Marvin & Orsingher, Enzo, 2023. "Pseudoprocesses related to higher-order equations of vibrations of rods," Statistics & Probability Letters, Elsevier, vol. 199(C).

    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. Lachal, Aimé, 2014. "First exit time from a bounded interval for pseudo-processes driven by the equation ∂/∂t=(−1)N−1∂2N/∂x2N," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1084-1111.
    2. Aimé Lachal, 2012. "A Survey on the Pseudo-process Driven by the High-order Heat-type Equation $\boldsymbol{\partial/\partial t=\pm\partial^N\!/\partial x^N}$ Concerning the Hitting and Sojourn Times," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 549-566, September.
    3. Mura, A. & Taqqu, M.S. & Mainardi, F., 2008. "Non-Markovian diffusion equations and processes: Analysis and simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5033-5064.
    4. D'Ovidio, Mirko & Orsingher, Enzo, 2011. "Bessel processes and hyperbolic Brownian motions stopped at different random times," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 441-465, March.

    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:125:y:2015:i:12:p:4455-4472. 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.