Parabolic Littlewood-Paley inequality for φ( - δ)-type operators and applications to stochastic integro-differential equations

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    Abstract

    In this paper we prove a parabolic version of the Littlewood-Paley inequality (1.4) for the operators of the type φ( - δ), where φ is a Bernstein function. As an application, we construct an L p-theory for the stochastic integro-differential equations of the type d u = ( - φ( - δ)u + f)d t + gdW t.

    Original languageEnglish
    Pages (from-to)161-203
    Number of pages43
    JournalAdvances in Mathematics
    Volume249
    DOIs
    Publication statusPublished - 2013 Dec 20

    Keywords

    • Estimates of transition functions
    • Integro-differential operators
    • Lévy processes
    • Parabolic Littlewood-Paley inequality
    • Stochastic partial differential equations

    ASJC Scopus subject areas

    • General Mathematics

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