IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v123y2013i2p446-474.html
   My bibliography  Save this article

On truncated variation, upward truncated variation and downward truncated variation for diffusions

Author

Listed:
  • Łochowski, Rafał M.
  • Miłoś, Piotr

Abstract

The truncated variation, TVc, is a fairly new concept introduced in Łochowski (2008) [5]. Roughly speaking, given a càdlàg function f, its truncated variation is “the total variation which does not pay attention to small changes of f, below some threshold c>0”. The very basic consequence of such approach is that contrary to the total variation, TVc is always finite. This is appealing to the stochastic analysis where so-far large classes of processes, like semimartingales or diffusions, could not be studied with the total variation. Recently in Łochowski (2011) [6], another characterization of TVc has been found. Namely TVc is the smallest possible total variation of a function which approximates f uniformly with accuracy c/2. Due to these properties we envisage that TVc might be a useful concept both in the theory and applications of stochastic processes.

Suggested Citation

  • Łochowski, Rafał M. & Miłoś, Piotr, 2013. "On truncated variation, upward truncated variation and downward truncated variation for diffusions," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 446-474.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:2:p:446-474
    DOI: 10.1016/j.spa.2012.08.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414912001743
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2012.08.007?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.

    Citations

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


    Cited by:

    1. Lesiba Ch. Galane & Rafa{l} M. {L}ochowski & Farai J. Mhlanga, 2017. "On the quadratic variation of the model-free price paths with jumps," Papers 1710.07894, arXiv.org, revised May 2018.
    2. Lifshits, Mikhail & Setterqvist, Eric, 2015. "Energy of taut strings accompanying Wiener process," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 401-427.
    3. Rafa{l} M. {L}ochowski & Nicolas Perkowski & David J. Promel, 2021. "One-dimensional game-theoretic differential equations," Papers 2101.08041, arXiv.org.

    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:123:y:2013:i:2:p:446-474. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.