Well-posedness for Stochastic Evolution Equations with Monotone Non-linearity and Multiplicative Poisson Noise in $L^p$

Erfan Salavati; Bijan Z. Zangeneh

Well-posedness for Stochastic Evolution Equations with Monotone Non-linearity and Multiplicative Poisson Noise in $L^p$

Probability 2016-12-28 v1

Authors: Erfan Salavati , Bijan Z. Zangeneh

Abstract

Semilinear stochastic evolution equations with L\'evy noise and monotone nonlinear drift are considered. The existence and uniqueness of the mild solutions in $L^p$ for these equations is proved and a sufficient condition for exponential asymptotic stability of the solutions is derived. The main tool in our study is an It\^o type inequality for the $p$ th power of stochastic convolution integrals in Hilbert spaces.

Keywords

stochastic evolution equations monotone nonlinearity Poisson noise Lévy noise mild solutions exponential stability Itô inequality

Cite

@article{arxiv.1612.08611,
  title  = {Well-posedness for Stochastic Evolution Equations with Monotone Non-linearity and Multiplicative Poisson Noise in $L^p$},
  author = {Erfan Salavati and Bijan Z. Zangeneh},
  journal= {arXiv preprint arXiv:1612.08611},
  year   = {2016}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1501.00402

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