A Maximal Inequality for pth Power of Stochastic Convolution Integrals

2015/01/02 by Erfan Salavati, Salavati, Erfan, Bijan Z. Zangeneh +1
Mathematics · #47H05 #47J35 #60G51 #60H10 #60H15 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:47H05 #msc:47J35 #msc:60G51 #msc:60H10 #msc:60H15

paper · pdf · doi:10.48550/arxiv.1501.00402

arxiv created 2015/01/02 · arxiv updated 2015/01/05

Abstract

An inequality for the pth 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 Lévy noise and monotone nonlinear drift. 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.

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