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arXiv · 2309.06316

Deterministic Integral and Ordinary Differential Equations over Irregular Paths

Yevgeniy Guseynov
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Abstract

We define a deterministic integral with respect to irregular paths as a limit of standard line integrals and completely describe a class of all paths for which this integral exists for functions with H\"older exponent in the range of (0,1]. With the developed integral calculus, we study the existence, uniqueness and continuity of solution of time- and path-dependent ordinary differential equations driven by irregular paths in traditional H\"older spaces. These results can be viewed as a supplement to the Young-Lyons-Gubinelli integration theory, in particular, for H\"older exponents less than 1/3.

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Yevgeniy Guseynov. 2023-09-12. Deterministic Integral and Ordinary Differential Equations over Irregular Paths. https://arxiv.org/abs/2309.06316

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