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

Erfan Salavati; Bijan Z. Zangeneh

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arXiv · 1612.08611

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

Erfan Salavati·Bijan Z. Zangeneh

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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.

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Erfan Salavati, Bijan Z. Zangeneh. 2016-11-19. Well-posedness for Stochastic Evolution Equations with Monotone Non-linearity and Multiplicative Poisson Noise in $L^p$. https://arxiv.org/abs/1612.08611

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