# Variability of paths and differential equations with $BV$-coefficients

@article{Hinz2020VariabilityOP, title={Variability of paths and differential equations with \$BV\$-coefficients}, author={Michael Hinz and Jonas M. Tolle and Lauri Viitasaari}, journal={arXiv: Probability}, year={2020} }

We define compositions $\varphi(X)$ of H\"older paths $X$ in $\mathbb{R}^n$ and functions of bounded variation $\varphi$ under a relative condition involving the path and the gradient measure of $\varphi$. We show the existence and properties of generalized Lebesgue-Stieltjes integrals of compositions $\varphi(X)$ with respect to a given H\"older path $Y$. These results are then used, together with Doss' transform, to obtain existence and, in a certain sense, uniqueness results for differential… CONTINUE READING

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