We study the existence and uniqueness of Lp-bounded mild solutions for a class ofsemilinear stochastic evolutions equations driven by a real L\'evy 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.

翻译：本文研究了一类由实值Lévy过程（无高斯分量且非平方可积，例如稳定过程）驱动的半线性随机演化方程的Lp有界温和解的存在唯一性问题。通过分离大小跳跃的截断方法，结合经典且简单的Banach不动点定理，在系数满足局部Lipschitz、Hölder和线性增长条件下，证明了该解的存在唯一性。