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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

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.

Suggested Citation

  • Kim, Kyeong-Hun & Kim, Panki, 2012. "An Lp-theory of a class of stochastic equations with the random fractional Laplacian driven by Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 122(12), pages 3921-3952.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:12:p:3921-3952
    DOI: 10.1016/j.spa.2012.08.001
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    References listed on IDEAS

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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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    Cited by:

    1. Kim, Ildoo & Kim, Kyeong-Hun, 2016. "An Lp-theory for stochastic partial differential equations driven by Lévy processes with pseudo-differential operators of arbitrary order," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2761-2786.

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