Article ID Journal Published Year Pages File Type
1155680 Stochastic Processes and their Applications 2012 32 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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