论文标题
二次变化的稳定性，并具有应用
Stability in quadratic variation, with applications
论文作者
论文摘要
我们表明，在\ cite {noncont}中定义的非连续dirichlet过程被关闭在局部Lipschitz连续地图（类似于\ cite {low}中所考虑的图中的时间均匀变体）下，从而扩展了定理2.1。从那篇论文。我们为这些转换提供了一个itô公式，并将其应用于研究$ [f（x^n）-f（x）] \ to $ x^n \ to x $（从某种意义上说）$ \ {x^n \} _ n $，$ x $以及某些本地lipschitz的持续图。我们还考虑$ [f_n（x^n）-f（x）] \ to 0 $ for $ c^1 $ maps $ \ {f_n \} _ n $，$ f $时，$ f_n'\ to f'to f'to f'$ complys comparts in Compacts。对于应用程序，我们提供了拆卸和集成剂稳定性的示例。
We show that non continuous Dirichlet processes, defined as in \cite{NonCont} are closed under a wide family of locally Lipschitz continuous maps (similar to the time-homogeneous variants of the maps considered in \cite{Low}) thus extending Theorem 2.1. from that paper. We provide an Itô formula for these transforms and apply it to study of how $[f(X^n)-f(X)]\to 0$ when $X^n\to X$ (in some appropriate sense) for certain Dirichlet processes $\{X^n\}_n$, $X$ and certain locally Lipschitz continuous maps. We also consider how $[f_n(X^n)-f(X)]\to 0$ for $C^1$ maps $\{f_n\}_n$, $f$ when $f_n'\to f'$ uniformly on compacts. For applications we give examples of jump removal and stability of integrators.
