An L-p-theory of a class of stochastic equations with the random fractional Laplacian driven by Levy processes

초록

In this paper we study some linear and quasi-linear stochastic equations with the random fractional Laplacian operator driven by arbitrary Levy 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. (C) 2012 Elsevier B.V. All rights reserved.

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