On path properties of certain infinitely divisible processes

Let {X(t): t [set membership, variant] T} be a stochastic process equal in distribution to {[integral operator]sf(t, s)[Lambda](ds): t [set membership, variant] T}, where [Lambda]is a symmetric independently scattered random measure and f is a suitable deterministic function. It is shown that various properties of the sections f(·,s), s [set membership, variant] S, are inherited by the sample paths of X, provided X has no Gaussian component. The analogous statement for Gaussian processes is false. As a main tool, LePage-type series representation is fully developed for symmetric stochastic integral processes and this may be of independent interest.