English

Parabolic Littlewood-Paley inequality for $\phi(-\Delta)$-type operators and applications to Stochastic integro-differential equations

Functional Analysis 2013-02-21 v1 Probability

Abstract

In this paper we prove a parabolic version of the Littlewood-Paley inequality for the operators of the type ϕ(Δ)\phi(-\Delta), where ϕ\phi is a Bernstein function. As an application, we construct an LpL_p-theory for the stochastic integro-differential equations of the type du=(ϕ(Δ)u+f)dt+gdWtdu=(-\phi(-\Delta)u+f)dt +gdW_t.

Keywords

Cite

@article{arxiv.1302.5053,
  title  = {Parabolic Littlewood-Paley inequality for $\phi(-\Delta)$-type operators and applications to Stochastic integro-differential equations},
  author = {Ildoo Kim and Kyeong-Hun Kim and Panki Kim},
  journal= {arXiv preprint arXiv:1302.5053},
  year   = {2013}
}