IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v115y2005i9p1487-1502.html
   My bibliography  Save this article

Reconstructing the drift of a diffusion from partially observed transition probabilities

Author

Listed:
  • Albeverio, S.
  • Marinelli, C.

Abstract

The problem of reconstructing the drift of a diffusion in , d[greater-or-equal, slanted]2, from the transition probability density observed outside a domain is considered. The solution of this problem also solves a new inverse problem for a class of parabolic partial differential equations. This work considerably extends [S. Albeverio et al. J. Statist. Phys. 57(1-2) (1989) 347-356] in terms of generality, both concerning assumptions on the drift coefficient, and allowing for non-constant diffusion coefficient. Sufficient conditions for solvability of this type of inverse problem for d=1 are also given.

Suggested Citation

  • Albeverio, S. & Marinelli, C., 2005. "Reconstructing the drift of a diffusion from partially observed transition probabilities," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1487-1502, September.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:9:p:1487-1502
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(05)00059-1
    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. Qian, Zhongmin & Zheng, Weian, 2004. "A representation formula for transition probability densities of diffusions and applications," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 57-76, May.
    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. Qian, Zhongmin & Xu, Xingcheng, 2023. "Probability bounds for reflecting diffusion processes," Statistics & Probability Letters, Elsevier, vol. 199(C).
    2. Taguchi, Dai & Tanaka, Akihiro, 2020. "Probability density function of SDEs with unbounded and path-dependent drift coefficient," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5243-5289.
    3. Zhongmin Qian & Yuhan Yao, 2022. "McKean–Vlasov type stochastic differential equations arising from the random vortex method," Partial Differential Equations and Applications, Springer, vol. 3(1), pages 1-22, February.
    4. Downes, A.N., 2009. "Bounds for the transition density of time-homogeneous diffusion processes," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 835-841, March.
    5. Song, Ruili & Ying, Jiangang, 2007. "A formula for transition density function under Girsanov transform," Statistics & Probability Letters, Elsevier, vol. 77(6), pages 658-666, 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:115:y:2005:i:9:p:1487-1502. 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.