Corpus ID: 214667009

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

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