Remarks on the factorization property of some random integrals

Two families of improper random integrals and the two corresponding convolution semigroups of infinitely divisible laws are studied. A relation (a factorization property) between those random integrals is established. For the proof we use the method of the random integral mappingsI(a,b]h,r that is also valid for infinitely divisible measures on Banach spaces. Furthermore, using that technique we established new relations between those two families of random integrals.