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

  • Mathematics(all)

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