IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-15358-7_11.html

Stochastic Integrals and SDE Driven by Nonlinear Lévy Noise

In: Stochastic Analysis 2010

Author

Listed:
  • Vassili N. Kolokoltsov

    (University of Warwick, Department of Statistics)

Abstract

We develop the theory of SDE driven by nonlinear Lévy noise, aiming at applications to Markov processes. It is shown that a conditionally positive integro-differential operator (of the Lévy–Khintchine type) with variable coefficients (diffusion, drift and Lévy measure) depending Lipschitz continuously on its parameters generates a Markov semigroup, where the measures are metricized by the Wasserstein–Kantorovich metrics W p . The analysis of SDE driven by nonlinear Lévy noise was initiated by the author in (“Kolokoltsov, Probability Theory Related Fields, DOI: 10.1007/s00440-010-0293-8, 2009”) (inspired partially by “Carmona and Nualart, Nonlinear Stochastic Integrators, Equations and Flows, Stochatic Monographs, v. 6, Gordon and Breach, 1990”), see also (“Kolokoltsov, Nonlinear Markov Processes and Kinetic Equations, Monograph. To appear in CUP, 2010”). Here, we suggest an alternative (seemingly more straightforward) approach based on the path-wise interpretation of these integrals as nonhomogeneous Lévy processes. Moreover, we are working with more general W p -distances rather than with W 2.

Suggested Citation

  • Vassili N. Kolokoltsov, 2011. "Stochastic Integrals and SDE Driven by Nonlinear Lévy Noise," Springer Books, in: Dan Crisan (ed.), Stochastic Analysis 2010, pages 227-242, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-15358-7_11
    DOI: 10.1007/978-3-642-15358-7_11
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:sprchp:978-3-642-15358-7_11. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.