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

Kyeong Hun Kim, Panki Kim

    Research output: Contribution to journalArticlepeer-review

    19 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)3921-3952
    Number of pages32
    JournalStochastic Processes and their Applications
    Volume122
    Issue number12
    DOIs
    Publication statusPublished - 2012 Dec

    Bibliographical note

    Funding Information:
    The research of the authors was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2011-0027230 ).

    Keywords

    • -theory
    • Fractional Laplacian
    • Lévy noise
    • Lévy processes
    • Stochastic partial differential equations
    • White noise

    ASJC Scopus subject areas

    • Statistics and Probability
    • Modelling and Simulation
    • Applied Mathematics

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