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Zero-One Laws for Multilinear Forms in Gaussian and Other Infinitely Divisible Random Variables

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  • Rosinski, J.
  • Samorodnitsky, G.
  • Taqqu, M. S.

Abstract

We establish zero-one laws for non-homogeneous forms of any finite order in Gaussian, non-Gaussian stable, or, more generally, in type G random variables. The random arguments in the form can be decoupled, totally coupled, or only partially coupled. These zero-one laws are applied to the study of sample paths of stochastic processes represented by multiple integrals.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:46:y:1993:i:1:p:61-82
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    Cited by:

    1. 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.
    2. Cambanis, Stamatis & Fotopoulos, Stergios B. & He, Lijian, 2000. "On the Conditional Variance for Scale Mixtures of Normal Distributions," Journal of Multivariate Analysis, Elsevier, vol. 74(2), pages 163-192, August.

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