English

A Maximal Inequality for $p$th Power of Stochastic Convolution Integrals

Probability 2015-01-05 v1

Abstract

An inequality for the ppth power of the norm of a stochastic convolution integral in a Hilbert space is proved. The inequality is stronger than analogues inequalities in the Literature in the sense that it is pathwise and not in expectation. An application of this inequality is provided for the semilinear stochastic evolution equations with L\'evy noise and monotone nonlinear drift. The existence and uniqueness of the mild solutions in LpL^p for these equations is proved and a sufficient condition for exponential asymptotic stability of the solutions is derived.

Keywords

Cite

@article{arxiv.1501.00402,
  title  = {A Maximal Inequality for $p$th Power of Stochastic Convolution Integrals},
  author = {Erfan Salavati and Bijan Z. Zangeneh},
  journal= {arXiv preprint arXiv:1501.00402},
  year   = {2015}
}
R2 v1 2026-06-22T07:49:11.874Z