KUKU

KU ScholarWorks

  • myKU
  • Email
  • Enroll & Pay
  • KU Directory
    • Login
    View Item 
    •   KU ScholarWorks
    • Mathematics
    • Mathematics Scholarly Works
    • View Item
    •   KU ScholarWorks
    • Mathematics
    • Mathematics Scholarly Works
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Large deviation for diffusions and Hamilton-Jacobi equation in Hilbert spaces

    Thumbnail
    View/Open
    FengJin_AP_34(1)321.pdf (561.5Kb)
    Issue Date
    2006-01-01
    Author
    Feng, Jin
    Publisher
    Institute of Mathematical Statistics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Metadata
    Show full item record
    Abstract
    Large deviation for Markov processes can be studied by Hamilton– Jacobi equation techniques. The method of proof involves three steps: First, we apply a nonlinear transform to generators of the Markov processes, and verify that limit of the transformed generators exists. Such limit induces a Hamilton–Jacobi equation. Second, we show that a strong form of uniqueness (the comparison principle) holds for the limit equation. Finally, we verify an exponential compact containment estimate. The large deviation principle then follows from the above three verifications. This paper illustrates such a method applied to a class of Hilbert-spacevalued small diffusion processes. The examples include stochastically perturbed Allen–Cahn, Cahn–Hilliard PDEs and a one-dimensional quasilinear PDE with a viscosity term.We prove the comparison principle using a variant of the Tataru method. We also discuss different notions of viscosity solution in infinite dimensions in such context.
    Description
    This is the published version, also available here: http://dx.doi.org/10.1214/009117905000000567.
    URI
    http://hdl.handle.net/1808/16715
    DOI
    https://doi.org/10.1214/009117905000000567
    Collections
    • Mathematics Scholarly Works [263]
    Citation
    Feng, Jin. "Large deviation for diffusions and Hamilton-Jacobi equation in Hilbert spaces." The Annals of Probability. (2006) 34, 1. 321-385. http://dx.doi.org/10.1214/009117905000000567.

    Items in KU ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.


    We want to hear from you! Please share your stories about how Open Access to this item benefits YOU.


    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

    Browse

    All of KU ScholarWorksCommunities & CollectionsThis Collection

    My Account

    LoginRegister

    Statistics

    View Usage Statistics

    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

    The University of Kansas
      Contact KU ScholarWorks
    Lawrence, KS | Maps
     
    • Academics
    • Admission
    • Alumni
    • Athletics
    • Campuses
    • Giving
    • Jobs

    The University of Kansas prohibits discrimination on the basis of race, color, ethnicity, religion, sex, national origin, age, ancestry, disability, status as a veteran, sexual orientation, marital status, parental status, gender identity, gender expression and genetic information in the University’s programs and activities. The following person has been designated to handle inquiries regarding the non-discrimination policies: Director of the Office of Institutional Opportunity and Access, IOA@ku.edu, 1246 W. Campus Road, Room 153A, Lawrence, KS, 66045, (785)864-6414, 711 TTY.

     Contact KU
    Lawrence, KS | Maps