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Teor. Veroyatnost. i Primenen., 1998, Volume 43, Issue 4, Pages 808–818 (Mi tvp2171)  

This article is cited in 5 scientific papers (total in 5 papers)

Short Communications

Representation of a class of semimartingales as stable integrals

P. A. Zanzotto

Dipartimento di Matematica, Università di Pisa, Italy

Abstract: We characterize the class of semimartingales which can be represented as a stochastic integral with respect to $\alpha$-stable Levy motion. Conditions are formulated in terms of the characteristics of the semimartingales.

Keywords: semimartingales without continuous martingale part, jump-measure, compensator, strictly $\alpha$-stable Levy processes, stable integrals, representation formulas.

DOI: https://doi.org/10.4213/tvp2171

Full text: PDF file (1406 kB)

English version:
Theory of Probability and its Applications, 1999, 43:4, 666–676

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Received: 12.01.1998
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Citation: P. A. Zanzotto, “Representation of a class of semimartingales as stable integrals”, Teor. Veroyatnost. i Primenen., 43:4 (1998), 808–818; Theory Probab. Appl., 43:4 (1999), 666–676

Citation in format AMSBIB
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\by P.~A.~Zanzotto
\paper Representation of~a~class of~semimartingales as~stable integrals
\jour Teor. Veroyatnost. i Primenen.
\yr 1998
\vol 43
\issue 4
\pages 808--818
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\crossref{https://doi.org/10.4213/tvp2171}
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\zmath{https://zbmath.org/?q=an:0956.60055}
\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 4
\pages 666--676
\crossref{https://doi.org/10.1137/S0040585X97977252}
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    This publication is cited in the following articles:
    1. Zanzotto P.A., “On stochastic differential equations driven by a Cauchy process and other stable Levy motions”, Annals of Probability, 30:2 (2002), 802–825  crossref  mathscinet  zmath  isi  scopus
    2. Theory Probab. Appl., 48:1 (2004), 181–188  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Kurenok V.P., “On driftless one–dimensional SDEs with respect to stable levy processes”, Lithuanian Mathematical Journal, 47:4 (2007), 423–435  crossref  mathscinet  isi  scopus
    4. Kurenok V., “A note on L–2–estimates for stable integrals with drift”, Transactions of the American Mathematical Society, 360:2 (2008), 925–938  crossref  mathscinet  zmath  isi  scopus
    5. Hu Ya., Long H., “Least squares estimator for Ornstein–Uhlenbeck processes driven by alpha–stable motions”, Stochastic Processes and Their Applications, 119:8 (2009), 2465–2480  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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