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A Vector Girsanov Result and its Applications to Conditional Measures via the Birkhoff Integrability

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Abstract

Some integration techniques for real-valued functions with respect to vector measures with values in Banach spaces (and vice versa) are investigated to establish abstract versions of classical theorems of probability and stochastic processes. In particular, the Girsanov Theorem is extended and used with the treated methods.

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Acknowledgements

The Fondo Ricerca di Base 2018 University of Perugia—and the GNAMPA—INDAM (Italy) Project “Metodi di Analisi Reale per l’Approssimazione attraverso operatori discreti e applicazioni” (2019) supported this research.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, University of Perugia, Via Vanvitelli, 1, 06123, Perugia, Italy

    Domenico Candeloro, Anna Rita Sambucini & Luca Trastulli

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  1. Domenico Candeloro
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  2. Anna Rita Sambucini
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  3. Luca Trastulli
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Correspondence to Anna Rita Sambucini.

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In memory of Domenico Candeloro who is for us, Master, Mentor and Friend, † May $$3^{\circ }$$3∘ 2019.

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Candeloro, D., Sambucini, A. . & Trastulli, L. A Vector Girsanov Result and its Applications to Conditional Measures via the Birkhoff Integrability. Mediterr. J. Math. 16, 144 (2019). https://doi.org/10.1007/s00009-019-1431-x

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  • DOI: https://doi.org/10.1007/s00009-019-1431-x

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