Variability and the existence of rough integrals with irregular coefficients

Michael Hinz; Jonas M. Tölle; Lauri Viitasaari

doi:10.1214/25-ECP656

Variability and the existence of rough integrals with irregular coefficients

Universität Bielefeld

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

40 Lataukset (Pure)

Abstrakti

Within the context of rough path analysis via fractional calculus, we show how variability can be used to prove the existence of integrals with respect to Hölder continuous multiplicative functionals in the case of Lipschitz coefficients with first order partial derivatives of bounded variation. We discuss applications to certain Gaussian processes, in particular, fractional Brownian motions with Hurst index 13<H≤12.

Alkuperäiskieli	Englanti
Sivut	1--12
Julkaisu	Electronic Communications in Probability
Vuosikerta	30
Numero	7
DOI - pysyväislinkit	https://doi.org/10.1214/25-ECP656
Tila	Julkaistu - 28 tammik. 2025
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Pääsy asiakirjaan

10.1214/25-ECP656

Variability and the existence of rough integrals with irregular coefficientsFinal published version, 288 KBLisenssi: CC BY

https://arxiv.org/abs/2407.06907Lisenssi: CC BY

Muut tiedostot ja linkit

Linkki julkaisuun Scopuksessa

Variability of paths and differential equations with BV-coefficients
Tölle, J. (Kutsuttu puhuja)
17 heinäk. 2024
Aktiviteetti: Kutsuttu akateeminen esitelmä

Lower path regularity in all dimensions
Hinz, M., Tölle, J. M. & Viitasaari, L., 28 toukok. 2026, (Jätetty) julkaisussa: arXiv.org. 25 Sivumäärä
Tutkimustuotos: Lehtiartikkeli › Article › Scientific
On fractal minimizers and potentials of occupation measures
Hinz, M., Tölle, J. M. & Viitasaari, L., 17 jouluk. 2025, (Jätetty) julkaisussa: arXiv.org. 28 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
6 Sitaatiot (Scopus)

66 Lataukset (Pure)

Siteeraa tätä

@article{f63c640dd6a8460a8d3857b6555aee07,

title = "Variability and the existence of rough integrals with irregular coefficients",

abstract = "Within the context of rough path analysis via fractional calculus, we show how variability can be used to prove the existence of integrals with respect to H{\"o}lder continuous multiplicative functionals in the case of Lipschitz coefficients with first order partial derivatives of bounded variation. We discuss applications to certain Gaussian processes, in particular, fractional Brownian motions with Hurst index 13",

keywords = "functions of bounded variation, Gaussian processes, fractional Brownian motion, variability, irregular multiplicative functionals, fractional rough path integrals",

author = "Michael Hinz and T{\"o}lle, \{Jonas M.\} and Lauri Viitasaari",

year = "2025",

month = jan,

day = "28",

doi = "10.1214/25-ECP656",

language = "English",

volume = "30",

pages = "1----12",

journal = "Electronic Communications in Probability",

issn = "1083-589X",

publisher = "Institute of Mathematical Statistics",

number = "7",

}

TY - JOUR

T1 - Variability and the existence of rough integrals with irregular coefficients

AU - Hinz, Michael

AU - Tölle, Jonas M.

AU - Viitasaari, Lauri

PY - 2025/1/28

Y1 - 2025/1/28

N2 - Within the context of rough path analysis via fractional calculus, we show how variability can be used to prove the existence of integrals with respect to Hölder continuous multiplicative functionals in the case of Lipschitz coefficients with first order partial derivatives of bounded variation. We discuss applications to certain Gaussian processes, in particular, fractional Brownian motions with Hurst index 13

AB - Within the context of rough path analysis via fractional calculus, we show how variability can be used to prove the existence of integrals with respect to Hölder continuous multiplicative functionals in the case of Lipschitz coefficients with first order partial derivatives of bounded variation. We discuss applications to certain Gaussian processes, in particular, fractional Brownian motions with Hurst index 13

KW - functions of bounded variation

KW - Gaussian processes

KW - fractional Brownian motion

KW - variability

KW - irregular multiplicative functionals

KW - fractional rough path integrals

UR - https://www.scopus.com/pages/publications/85217502246

U2 - 10.1214/25-ECP656

DO - 10.1214/25-ECP656

M3 - Article

SN - 1083-589X

VL - 30

SP - 1

EP - 12

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

IS - 7

ER -

Variability and the existence of rough integrals with irregular coefficients

Abstrakti

Pääsy asiakirjaan

Muut tiedostot ja linkit

Sormenjälki

Aktiviteetit

Variability of paths and differential equations with BV-coefficients

Tutkimustuotos

Lower path regularity in all dimensions

On fractal minimizers and potentials of occupation measures

Variability of paths and differential equations with BV-coefficients

Siteeraa tätä