On bounded mild solutions for a class of semilinear stochastic evolution equation driven by stable process

2020/02/19 by Manou-Abi, Solym M.
#34 F05 #60G46 #60G52 #60H30 #65C30 #F.2.2 #FOS: Mathematics #I.2.7 #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2002.08100

Abstract

We study the existence and uniqueness of Lp-bounded mild solutions for a class ofsemilinear stochastic evolutions equations driven by a real Lévy processes withoutGaussian component not square integrable for instance the stable process through atruncation method by separating the big and small jumps together with the classicaland simple Banach fixed point theorem ; under local Lipschitz, Holder, linear growthconditions on the coefficients.

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