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

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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Year of publication:	2012
Authors:	Kim, Kyeong-Hun ; Kim, Panki
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 122.2012, 12, p. 3921-3952
Publisher:	Elsevier
Subject:	Fractional Laplacian \| Stochastic partial differential equations \| Lévy processes \| Lp-theory \| White noise \| Lévy noise

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10010580873