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Existence and Uniqueness of Solutions of Differential Equations Weakly Controlled by Rough Paths with an Arbitrary Positive Hölder Exponent

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Abstract

A functional version of the theory of rough paths with an arbitrary Hölder exponent is developed. It is used to prove a theorem on the existence and uniqueness of a solution for the class of ordinary and the class of stochastic one-dimensional differential equations weakly controlled by rough paths with an arbitrary Hölder exponent and to obtain a change of variables formula for the equations in the first of these two classes.

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Authors and Affiliations

  1. Belarusian State University, Minsk, 220030, Belarus

    M. M. Vas’kovskii

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  1. M. M. Vas’kovskii
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Correspondence to M. M. Vas’kovskii.

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Translated by V. Potapchouck

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Vas’kovskii, M.M. Existence and Uniqueness of Solutions of Differential Equations Weakly Controlled by Rough Paths with an Arbitrary Positive Hölder Exponent. Diff Equat 57, 1279–1291 (2021). https://doi.org/10.1134/S0012266121100025

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  • DOI: https://doi.org/10.1134/S0012266121100025

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