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.

    Evolution equation of a stochastic semigroup with white-noise drift

    Thumbnail
    View/Open
    NualartD_AP_28(1)36.pdf (254.0Kb)
    Issue Date
    2000-09-20
    Author
    Nualart, David
    Viens, Frederi
    Publisher
    Institute of Mathematical Statistics (IMS)
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Metadata
    Show full item record
    Abstract
    We study the existence and uniqueness of the solution of a function-valued stochastic evolution equation based on a stochastic semigroup whose kernel p(s,t,y,x) is Brownian in s and t.The kernel p is supposed to be measurable with respect to the increments of an underlying Wiener process in the interval [s,t]. The evolution equation is then anticipative and, choosing the Skorohod formulation,we establish existence and uniqueness of a continuous solution with values in L2(Rd).

    As an application we prove the existence of a mild solution of the stochastic parabolic equation

    du_t = \Delta_x u dt + v(dt, x) \cdot \nabla u + F(t, x, u) W(dt, x),

    where v and W are Brownian in time with respect to a common filtration. In this case, p is the formal backward heat kernel of Δx+v(dt,x)⋅∇x .
    Description
    This is the published version, also available here: http://dx.doi.org/10.1214/aop/1019160111.
    URI
    http://hdl.handle.net/1808/17053
    DOI
    https://doi.org/10.1214/aop/1019160111
    Collections
    • Mathematics Scholarly Works [282]
    Citation
    Nualart, David; Viens, Frederi. Evolution equation of a stochastic semigroup with white-noise drift. Ann. Probab. 28 (2000), no. 1, 36--73. http://dx.doi.org/10.1214/aop/1019160111.

    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