On path properties of certain infinitely divisible processes

Jan Rosinski

Stochastic Processes and their Applications, 1989, vol. 33, issue 1, 73-87

Abstract: 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.

Keywords: infinitely; divisible; processes; sample; path; properties; series; and; stochastic; integral; representations; of; infinitely; divisible; processes (search for similar items in EconPapers)
Date: 1989
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Citations: View citations in EconPapers (2)

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