论文标题
Skorohod-Wichura定理的详细和直接证明
A detailed and direct proof of Skorohod-Wichura's theorem
论文作者
论文摘要
在公制空间上随机变量弱收敛性的Skorohod定理可以追溯到Skorohod（1956），如果公制空间是[0,1]上定义的真实价值函数类别的情况，这些函数是右连续的，并且在Skorohod Metric赋予左手时，则具有左侧限制。在公制空间的扩展中，Wichura（1970）的版本似乎是最基本的。但是，维古拉的证据似乎注定为一个非常有限的公众。我们提出了一个更详细的证据，以使其在研究生级别更容易获得。但是，由于原始证明中的重要步骤被删除，我们可以通过简化它来做更多的事情，这导致了直接的证据，我们希望对更大的读者更容易理解。当前版本更适合不同种类的概括。
The representation Skorohod theorem of weak convergence of random variables on a metric space goes back to Skorohod (1956) in the case where the metric space is the class of real-valued functions defined on [0,1] which are right-continuous and have left-hand limits when endowed with the Skorohod metric. Among the extensions of that to metric spaces, the version by Wichura (1970) seems to be the most fundamental. But the proof of Wichura seems to be destined to a very restricted public. We propose a more detailed proof to make it more accessible at the graduate level. However we do far more by simplifying it since important steps in the original proof are dropped, which leads to a direct proof that we hope to be more understandable to a larger spectrum of readers. The current version is more appropriate for different kinds of generalizations.
