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On path properties of certain infinitely divisible processes

Author

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  • Rosinski, Jan

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.

Suggested Citation

  • Rosinski, Jan, 1989. "On path properties of certain infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 73-87, October.
    • Handle: RePEc:eee:spapps:v:33:y:1989:i:1:p:73-87
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    Cited by:

    1. Sauri, Orimar & Veraart, Almut E.D., 2017. "On the class of distributions of subordinated Lévy processes and bases," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 475-496.

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