论文标题
$ bv $ - 系数的路径和微分方程的可变性
Variability of paths and differential equations with $BV$-coefficients
论文作者
论文摘要
我们定义了hölder路径的$φ（x）$ x $ in $ \ mathbb {r}^n $和有限变化$φ$的函数，涉及路径和梯度度量$φ$的梯度。我们展示了与给定的Hölder路径$ y $相对于构图$φ（x）$的广义lebesgue-stieltjes积分的存在和属性。然后将这些结果与Doss的变换一起使用，以获得存在，从某种意义上说，在$ \ Mathbb {r}^n $中，由Hölder路径驱动的唯一方程式结果，并涉及有限变化的系数。示例包括具有不连续系数的方程式，该方程是由二维布朗动作的路径驱动的。
We define compositions $φ(X)$ of Hölder paths $X$ in $\mathbb{R}^n$ 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 $\mathbb{R}^n$ 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.
