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

2016/11/19 by Salavati, Erfan, Zangeneh, Bijan Z.
#47H05 #47J35 #60G51 #60H10 #60H15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1612.08611

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 pth power of stochastic convolution integrals in Hilbert spaces.

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