Variability of paths and differential equations with BV-coefficients
Hinz M, Tölle JM, Viitasaari L (2023)
Annales de l'Institut Henri Poincaré (B): Probability and Statistics 59(4): 2036-2082.
Zeitschriftenaufsatz
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Autor*in
Hinz, MichaelUniBi;
Tölle, Jonas M.;
Viitasaari, Lauri
Einrichtung
Abstract / Bemerkung
We define compositions phi(X) of Holder paths X in Rn and functions of bounded variation phi under a relative condition involving the path and the gradient measure of phi. We show the existence and properties of generalized Lebesgue-Stieltjes integrals of compositions phi (X) with respect to a given Holder path Y. These results are then used, together with Doss' transform, to obtain existence and, in a certain sense, uniqueness results for differential equations in Rn driven by Holder paths and involving coefficients of bounded variation. Examples include equations with discontinuous coefficients driven by paths of two-dimensional fractional Brownian motions.
Stichworte
Functions of bounded variation;
Generalized Lebesgue-Stieltjes;
integrals;
Occupation measure;
Holder path;
Riesz potential;
Systems of;
nonlinear differential equations
Erscheinungsjahr
2023
Zeitschriftentitel
Annales de l'Institut Henri Poincaré (B): Probability and Statistics
Band
59
Ausgabe
4
Seite(n)
2036-2082
ISSN
0246-0203
Page URI
https://pub.uni-bielefeld.de/record/2984907
Zitieren
Hinz M, Tölle JM, Viitasaari L. Variability of paths and differential equations with BV-coefficients. Annales de l'Institut Henri Poincaré (B): Probability and Statistics . 2023;59(4):2036-2082.
Hinz, M., Tölle, J. M., & Viitasaari, L. (2023). Variability of paths and differential equations with BV-coefficients. Annales de l'Institut Henri Poincaré (B): Probability and Statistics , 59(4), 2036-2082. https://doi.org/10.1214/22-AIHP1308
Hinz, Michael, Tölle, Jonas M., and Viitasaari, Lauri. 2023. “Variability of paths and differential equations with BV-coefficients”. Annales de l'Institut Henri Poincaré (B): Probability and Statistics 59 (4): 2036-2082.
Hinz, M., Tölle, J. M., and Viitasaari, L. (2023). Variability of paths and differential equations with BV-coefficients. Annales de l'Institut Henri Poincaré (B): Probability and Statistics 59, 2036-2082.
Hinz, M., Tölle, J.M., & Viitasaari, L., 2023. Variability of paths and differential equations with BV-coefficients. Annales de l'Institut Henri Poincaré (B): Probability and Statistics , 59(4), p 2036-2082.
M. Hinz, J.M. Tölle, and L. Viitasaari, “Variability of paths and differential equations with BV-coefficients”, Annales de l'Institut Henri Poincaré (B): Probability and Statistics , vol. 59, 2023, pp. 2036-2082.
Hinz, M., Tölle, J.M., Viitasaari, L.: Variability of paths and differential equations with BV-coefficients. Annales de l'Institut Henri Poincaré (B): Probability and Statistics . 59, 2036-2082 (2023).
Hinz, Michael, Tölle, Jonas M., and Viitasaari, Lauri. “Variability of paths and differential equations with BV-coefficients”. Annales de l'Institut Henri Poincaré (B): Probability and Statistics 59.4 (2023): 2036-2082.
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