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Spectral representation of semistable processes, and semistable laws on Banach spaces

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  • Rajput, Balram S.
  • Rama-Murthy, Kavi

Abstract

We introduce the notion of semistable processes and semistable random measures; and give a characterization of semistable laws on Banach spaces. Using this charcterization, we discuss the existence of semistable random measures, define the stochastic integrals with respect to these measures, and obtain the spectral representations of arbitrary (not necessairly symmetric) semistable and stable processes. In addition, we give a criterion of independence for stochastic integrals.

Suggested Citation

  • Rajput, Balram S. & Rama-Murthy, Kavi, 1987. "Spectral representation of semistable processes, and semistable laws on Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 21(1), pages 139-157, February.
    • Handle: RePEc:eee:jmvana:v:21:y:1987:i:1:p:139-157
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    Citations

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    Cited by:

    1. Makoto Maejima & Gennady Samorodnitsky, 1999. "Certain Probabilistic Aspects of Semistable Laws," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(3), pages 449-462, September.
    2. Balram S. Rajput & Kavi Rama-Murthy, 2007. "Uniform Comparison of Tails of (Non-Symmetric) Probability Measures and Their Symmetrized Counterparts with Applications," Journal of Theoretical Probability, Springer, vol. 20(1), pages 87-105, March.
    3. Makoto Maejima & Ken-iti Sato, 1999. "Semi-Selfsimilar Processes," Journal of Theoretical Probability, Springer, vol. 12(2), pages 347-373, April.

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