Sobolev regularity of occupation measures and paths, variability and compositions

Michael Hinz; Jonas M. Tölle; Lauri Viitasaari

doi:10.1214/22-EJP797

Sobolev regularity of occupation measures and paths, variability and compositions

Michael Hinz, Jonas M. Tölle, Lauri Viitasaari

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

4 Sitaatiot (Scopus)

75 Lataukset (Pure)

Abstrakti

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 Lévy processes, and we use it to show the existence of Stieltjes type integrals involving compositions.

Alkuperäiskieli	Englanti
Artikkeli	73
Sivut	1–29
Julkaisu	Electronic Journal of Probability
Vuosikerta	27
Numero	73
DOI - pysyväislinkit	https://doi.org/10.1214/22-EJP797
Tila	Julkaistu - 15 kesäk. 2022
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Pääsy asiakirjaan

10.1214/22-EJP797Lisenssi: CC BY

SCI_Hinz_etal_EJP_2022Final published version, 412 KBLisenssi: CC BY

https://arxiv.org/abs/2105.06249

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Linkki julkaisuun Scopuksessa

3 Kutsuttu akateeminen esitelmä
1 Konferenssiesitelmä
1 Vierailu ulkomaiseen yliopistoon

Variability of paths and differential equations with BV-coefficients
Tölle, J. (Puhuja)
21 syysk. 2023
Aktiviteetti: Kutsuttu akateeminen esitelmä
Variability of paths and differential equations with BV-coefficients
Jonas Tölle (Kutsuttu puhuja)
25 marrask. 2022
Aktiviteetti: Kutsuttu akateeminen esitelmä
Variability of functions, compositions and differential equations with BV-coefficients
Jonas Tölle (Kutsuttu puhuja)
21 helmik. 2022
Aktiviteetti: Kutsuttu akateeminen esitelmä

4 Viittaukset
2 Article

Variability and the existence of rough integrals with irregular coefficients
Hinz, M., Tölle, J. M. & Viitasaari, L., 10 heinäk. 2024, (Jätetty) julkaisussa: arXiv.org. 13 Sivumäärä
Tutkimustuotos: Lehtiartikkeli › Article › Scientific
Variability of paths and differential equations with BV-coefficients
Hinz, M., Tölle, J. M. & Viitasaari, L., 4 marrask. 2023, julkaisussa: Annales de l'Institut Henri Poincaré B, Probabilités et Statistiques. 59, 4, s. 2036–2082 46 Sivumäärä
Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

Open access
Tiedosto
2 Sitaatiot (Scopus)

54 Lataukset (Pure)

Siteeraa tätä

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title = "Sobolev regularity of occupation measures and paths, variability and compositions",

abstract = "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{\'e}vy processes, and we use it to show the existence of Stieltjes type integrals involving compositions.",

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AU - Tölle, Jonas M.

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N2 - 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 Lévy processes, and we use it to show the existence of Stieltjes type integrals involving compositions.

AB - 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 Lévy processes, and we use it to show the existence of Stieltjes type integrals involving compositions.

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Sobolev regularity of occupation measures and paths, variability and compositions

Abstrakti

Pääsy asiakirjaan

Muut tiedostot ja linkit

Sormenjälki

Aktiviteetit

Variability of paths and differential equations with BV-coefficients

Variability of paths and differential equations with BV-coefficients

Variability of functions, compositions and differential equations with BV-coefficients

Tutkimustuotos

Variability and the existence of rough integrals with irregular coefficients

Variability of paths and differential equations with BV-coefficients

Siteeraa tätä