### Sobolev regularity of occupation measures and paths, variability and compositions

Hinz M, Tolle JM, Viitasaari L (2022)
Electronic Journal of Probability 27: 73.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Hinz, MichaelUniBi; Tolle, Jonas M.; Viitasaari, Lauri
Einrichtung
Abstract / Bemerkung
We prove a result on the fractional Sobolev regularity of composition of paths of low fractional Sobolev regularity with functions of bounded variation. The result relies on the notion of variability, proposed by us in the previous article [43]. Here we work under relaxed hypotheses, formulated in terms of Sobolev norms, and we can allow discontinuous paths, which is new. The result applies to typical realizations of certain Gaussian or L??vy processes, and we use it to show the existence of Stieltjes type integrals involving compositions.
Stichworte
occupation measures; local times; fractional Sobolev regularity; functions of bounded variation; compositions
Erscheinungsjahr
2022
Zeitschriftentitel
Electronic Journal of Probability
Band
27
Art.-Nr.
73
eISSN
1083-6489
Page URI
https://pub.uni-bielefeld.de/record/2964348

### Zitieren

Hinz M, Tolle JM, Viitasaari L. Sobolev regularity of occupation measures and paths, variability and compositions. Electronic Journal of Probability . 2022;27: 73.
Hinz, M., Tolle, J. M., & Viitasaari, L. (2022). Sobolev regularity of occupation measures and paths, variability and compositions. Electronic Journal of Probability , 27, 73. https://doi.org/10.1214/22-EJP797
Hinz, M., Tolle, J. M., and Viitasaari, L. (2022). Sobolev regularity of occupation measures and paths, variability and compositions. Electronic Journal of Probability 27:73.
Hinz, M., Tolle, J.M., & Viitasaari, L., 2022. Sobolev regularity of occupation measures and paths, variability and compositions. Electronic Journal of Probability , 27: 73.
M. Hinz, J.M. Tolle, and L. Viitasaari, “Sobolev regularity of occupation measures and paths, variability and compositions”, Electronic Journal of Probability , vol. 27, 2022, : 73.
Hinz, M., Tolle, J.M., Viitasaari, L.: Sobolev regularity of occupation measures and paths, variability and compositions. Electronic Journal of Probability . 27, : 73 (2022).
Hinz, Michael, Tolle, Jonas M., and Viitasaari, Lauri. “Sobolev regularity of occupation measures and paths, variability and compositions”. Electronic Journal of Probability 27 (2022): 73.

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