Variability of paths and differential equations with BV-coefficients
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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en
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46
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Annales de l'Institut Henri Poincaré B: Probabilités et Statistiques, Volume 59, issue 4, pp. 2036–2082
Abstract
We define compositions φ(X) of Hölder paths X in ℝn and functions of bounded variation φ under a relative condition involving the path and the gradient measure of φ. We show the existence and properties of generalized Lebesgue-Stieltjes integrals of compositions φ(X) with respect to a given Hölder 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 Hölder paths and involving coefficients of bounded variation. Examples include equations with discontinuous coefficients driven by paths of two-dimensional fractional Brownian motions.Description
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Hinz, M, Tölle, J M & Viitasaari, L 2023, 'Variability of paths and differential equations with BV-coefficients', Annales de l'Institut Henri Poincaré B: Probabilités et Statistiques, vol. 59, no. 4, pp. 2036–2082. https://doi.org/10.1214/22-AIHP1308