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Symmetric infinitely divisible processes with sample paths in Orlicz spaces and absolute continuity of infinitely divisible processes

Author

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  • Braverman, Michael
  • Samorodnitsky, Gennady

Abstract

We give necessary and sufficient conditions under which a symmetric measurable infinitely divisible process has sample paths in an Orlicz space L[psi] with a function [psi] satisfying the [Delta]2 condition and, as an application, obtain necessary and sufficient conditions for a symmetric infinitely divisible process to have a version with absolutely continuous paths.

Suggested Citation

  • Braverman, Michael & Samorodnitsky, Gennady, 1998. "Symmetric infinitely divisible processes with sample paths in Orlicz spaces and absolute continuity of infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 78(1), pages 1-26, October.
    • Handle: RePEc:eee:spapps:v:78:y:1998:i:1:p:1-26
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    Cited by:

    1. Andreas Basse-O'Connor & Raphaël Lachièze-Rey & Mark Podolskij, 2015. "Limit theorems for stationary increments Lévy driven moving averages," CREATES Research Papers 2015-56, Department of Economics and Business Economics, Aarhus University.
    2. Basse, Andreas & Pedersen, Jan, 2009. "Lévy driven moving averages and semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2970-2991, September.
    3. Sauri, Orimar, 2020. "On the divergence and vorticity of vector ambit fields," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6184-6225.

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