Cameron-Martin type theorem for a class of non-Gaussian measures
da Silva JL, Erraoui M, Röckner M (2024)
Stochastic Analysis and Applications .
Zeitschriftenaufsatz
| E-Veröff. vor dem Druck | Englisch
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Autor*in
da Silva, J. L.;
Erraoui, M.;
Röckner, MichaelUniBi
Einrichtung
Abstract / Bemerkung
In this article, we study the quasi-translation-invariant property of a class of non-Gaussian measures. These measures are associated with the family of generalized grey Brownian motions. We identify the Cameron-Martin space and derive the explicit Radon-Nikodym density in terms of the Wiener integral with respect to the fractional Brownian motion. Moreover, we show an integration by parts formula for the derivative operator in the directions of the Cameron-Martin space. As a consequence, we derive the closability of both the derivative and the corresponding gradient operators.
Stichworte
Fractional Brownian motion;
Cameron-Martin theorem;
generalized grey;
Brownian motion;
subordination;
integration by parts
Erscheinungsjahr
2024
Zeitschriftentitel
Stochastic Analysis and Applications
ISSN
0736-2994
eISSN
1532-9356
Page URI
https://pub.uni-bielefeld.de/record/2992558
Zitieren
da Silva JL, Erraoui M, Röckner M. Cameron-Martin type theorem for a class of non-Gaussian measures. Stochastic Analysis and Applications . 2024.
da Silva, J. L., Erraoui, M., & Röckner, M. (2024). Cameron-Martin type theorem for a class of non-Gaussian measures. Stochastic Analysis and Applications . https://doi.org/10.1080/07362994.2024.2389133
da Silva, J. L., Erraoui, M., and Röckner, Michael. 2024. “Cameron-Martin type theorem for a class of non-Gaussian measures”. Stochastic Analysis and Applications .
da Silva, J. L., Erraoui, M., and Röckner, M. (2024). Cameron-Martin type theorem for a class of non-Gaussian measures. Stochastic Analysis and Applications .
da Silva, J.L., Erraoui, M., & Röckner, M., 2024. Cameron-Martin type theorem for a class of non-Gaussian measures. Stochastic Analysis and Applications .
J.L. da Silva, M. Erraoui, and M. Röckner, “Cameron-Martin type theorem for a class of non-Gaussian measures”, Stochastic Analysis and Applications , 2024.
da Silva, J.L., Erraoui, M., Röckner, M.: Cameron-Martin type theorem for a class of non-Gaussian measures. Stochastic Analysis and Applications . (2024).
da Silva, J. L., Erraoui, M., and Röckner, Michael. “Cameron-Martin type theorem for a class of non-Gaussian measures”. Stochastic Analysis and Applications (2024).
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