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

Abstract

Semilinear stochastic evolution equations with Lévy 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 Itô type inequality for the $p$th power of stochastic convolution integrals in Hilbert spaces.

arXiv admin note: substantial text overlap with arXiv:1501.00402

References in corpus (3)

• Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise
• Continuous Dependence on Coefficients for Stochastic Evolution Equations with Multiplicative Lévy Noise and Monotone Nonlinearity
• Stochastic Evolution Equations with Multiplicative Poisson Noise and Monotone Nonlinearity: A New Approach