On series representations of infinitely divisible random vectors (Q914228)

Let \(\{\tau_ j\}\) be a sequence of arrival times in a Poisson process, \(\{\xi_ j\}\) a sequence of iid random elements, independent of \(\{\tau_ j\}\), and H a Banach space valued function. The paper studies the convergence and limit distributions of centered sums of the form \[ \sum^{n}_{j=1}H(\tau_ j,\xi_ j)-A_ n. \] Generalizations of LePage's representations are obtained in a unified way. Certain conditionally Gaussian infinitely divisible random vectors are characterized.