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An Lp-theory of a class of stochastic equations with the random fractional Laplacian driven by Lévy processes

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  • Kim, Kyeong-Hun
  • Kim, Panki
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    Abstract

    In this paper we study some linear and quasi-linear stochastic equations with the random fractional Laplacian operator driven by arbitrary Lévy processes. The driving noise can be space–time in the case of one dimensional spacial variable. We prove uniqueness and existence of such equations in Sobolev spaces. Out results cover the case when the driving noise is a space–time white noise.

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    Bibliographic Info

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

    Volume (Year): 122 (2012)
    Issue (Month): 12 ()
    Pages: 3921-3952

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:12:p:3921-3952

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    Related research

    Keywords: Fractional Laplacian; Stochastic partial differential equations; Lévy processes; Lp-theory; White noise; Lévy noise;

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    1. Mikulevicius, R. & Pragarauskas, H., 2009. "On Hölder solutions of the integro-differential Zakai equation," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3319-3355, October.
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