  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.
