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Path and semimartingale properties of chaos processes

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  • Basse-O'Connor, Andreas
  • Graversen, Svend-Erik

Abstract

The present paper characterizes various properties of chaos processes which in particular include processes where all time variables admit a Wiener chaos expansion of a fixed finite order. The main focus is on the semimartingale property, p-variation and continuity. The general results obtained are finally used to characterize when a moving average is a semimartingale.

Suggested Citation

  • Basse-O'Connor, Andreas & Graversen, Svend-Erik, 2010. "Path and semimartingale properties of chaos processes," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 522-540, April.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:4:p:522-540
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    References listed on IDEAS

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    1. Cambanis, Stamatis & Nolan, John P. & Rosinski, Jan, 1990. "On the oscillation of infinitely divisible and some other processes," Stochastic Processes and their Applications, Elsevier, vol. 35(1), pages 87-97, June.
    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. Pérez-Abreu, Victor & Rocha-Arteaga, Alfonso, 1997. "On stable processes of bounded variation," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 69-77, April.
    4. Rosinski, J. & Samorodnitsky, G. & Taqqu, M. S., 1993. "Zero-One Laws for Multilinear Forms in Gaussian and Other Infinitely Divisible Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 46(1), pages 61-82, July.
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