论文标题
控制的微分方程作为粗糙积分
Controlled differential equations as rough integrals
论文作者
论文摘要
我们研究具有无限漂移术语的受控微分方程，其中驱动路径为$ν$-Hölder连续$ν\ in（\ frac {1} {3}，\ frac {1} {2} {2}）$，因此在Gubinelli Sense sense \ cote {gubinelli parts中解释了粗糙的积分。类似于Lyons \ Cite {Lyons98}或Friz-Victoir \ cite {friz}的粗糙微分方程，我们证明了Gubinelli的解决方案的存在和唯一性定理，Gubinelli的意义，最初的值和解决方案规范估算值。
We study controlled differential equations with unbounded drift terms, where the driving paths is $ν$ - Hölder continuous for $ν\in (\frac{1}{3},\frac{1}{2})$, so that the rough integral are interpreted in the Gubinelli sense \cite{gubinelli} for controlled rough paths. Similar to the rough differential equations in the sense of Lyons \cite{lyons98} or of Friz-Victoir \cite{friz}, we prove the existence and uniqueness theorem for the solution in the sense of Gubinelli, the continuity on the initial value, and the solution norm estimates.
