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An L-p-theory of a class of stochastic equations with the random fractional Laplacian driven by Levy processes
- Authors
- Kim, Kyeong-Hun; Kim, Panki
- Issue Date
- 12월-2012
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- Fractional Laplacian; Stochastic partial differential equations; Levy processes; L-p-theory; White noise; Levy noise
- Citation
- STOCHASTIC PROCESSES AND THEIR APPLICATIONS, v.122, no.12, pp.3921 - 3952
- Indexed
- SCIE
SCOPUS
- Journal Title
- STOCHASTIC PROCESSES AND THEIR APPLICATIONS
- Volume
- 122
- Number
- 12
- Start Page
- 3921
- End Page
- 3952
- ISSN
- 0304-4149
- Abstract
- 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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