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Solving a non-linear stochastic pseudo-differential equation of Burgers type

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  • Jacob, Niels
  • Potrykus, Alexander
  • Wu, Jiang-Lun
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    Abstract

    In this paper, we study the initial value problem for a class of non-linear stochastic equations of Burgers type of the following form [not partial differential]tu+q(x,D)u+[not partial differential]xf(t,x,u)=h1(t,x,u)+h2(t,x,u)Ft,x for , where q(x,D) is a pseudo-differential operator with negative definite symbol of variable order which generates a stable-like process with transition density, are measurable functions, and Ft,x stands for a Lévy space-time white noise. We investigate the stochastic equation on the whole space in the mild formulation and show the existence of a unique local mild solution to the initial value problem by utilising a fixed point argument.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 120 (2010)
    Issue (Month): 12 (December)
    Pages: 2447-2467

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    Handle: RePEc:eee:spapps:v:120:y:2010:i:12:p:2447-2467

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    Related research

    Keywords: Non-linear stochastic pseudo-differential equations Lévy space-time white noise Transition density Mild equations;

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