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A Girsanov Result Through Birkhoff Integral

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Computational Science and Its Applications – ICCSA 2018 (ICCSA 2018)

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Abstract

A vector-valued version of the Girsanov theorem is presented, for a scalar process with respect to a Banach-valued measure. Previously, a short discussion about the Birkhoff-type integration is outlined, as for example integration by substitution, in order to fix the measure-theoretic tools needed for the main result, Theorem 6, where a martingale equivalent to the underlying vector probability has been obtained in order to represent the modified process as a martingale with the same marginals as the original one.

Anna Rita Sambucini: The authors have been supported by Fondo Ricerca di Base 2015 University of Perugia - titles: “\(L^p\) Spaces in Banach Lattices with applications”, “The Choquet integral with respect to fuzzy measures and applications” and by Grant Prot. N. U UFMBAZ2017/0000326 of GNAMPA – INDAM (Italy).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, Perugia, Italy

    Domenico Candeloro & Anna Rita Sambucini

Authors
  1. Domenico Candeloro
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  2. Anna Rita Sambucini
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Correspondence to Anna Rita Sambucini .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  5. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

  6. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  7. Monash University, Clayton, Victoria, Australia

    David Taniar

  8. Kyushu Sangyo University, Fukuoka shi, Fukuoka, Japan

    Bernady O. Apduhan

  9. Politecnico di Bari, Bari, Italy

    Eufemia Tarantino

  10. Myongji University, Yongin, Korea (Republic of)

    Yeonseung Ryu

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Candeloro, D., Sambucini, A.R. (2018). A Girsanov Result Through Birkhoff Integral. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2018. ICCSA 2018. Lecture Notes in Computer Science(), vol 10960. Springer, Cham. https://doi.org/10.1007/978-3-319-95162-1_47

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  • DOI: https://doi.org/10.1007/978-3-319-95162-1_47

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