论文标题
复制及其应用于弱收敛
Replication and Its Application to Weak Convergence
论文作者
论文摘要
本文中，开发了一种方法来将功能，衡量和随机过程复制到紧凑的度量空间。许多结果很容易为复制对象建立，然后转回原始对象。在其中解决了两个问题以证明该方法：（1）生活在一般拓扑空间上的过程的有限维收敛。 （2）Skorokhod空间$ d（\ Mathbf {r}^{+}; e $作为一般的Tychonoff空间，给出了Skorokhod空间$ d（\ Mathbf {r}^{+}; e）的新紧密度和相对紧凑的标准。此处的方法还用于同伴论文中来建立以下方法：（3）存在，与Martingale问题解决方案的独特性和收敛性，（4）经典的Fujisaki-Kallianpur-Kunita和Duncan-Mortensen-Zakai-Zakai-Zakai-Zakai-Zakai-Zakai-Zakai滤波器方程式和固定过滤器，（5）最有限的信号测量值（5）6个标记（5）标记（5）标记（5）标记（5）标记（5）标记（5）piert to（5）piever to（5）piever to（5）。过程，（7）射线骑士理论都在一般环境中。
Herein, a methodology is developed to replicate functions, measures and stochastic processes onto a compact metric space. Many results are easily established for the replica objects and then transferred back to the original ones. Two problems are solved within to demonstrate the method: (1) Finite-dimensional convergence for processes living on general topological spaces. (2) New tightness and relative compactness criteria are given for the Skorokhod space $D(\mathbf{R}^{+};E)$ with $E$ being a general Tychonoff space. The methods herein are also used in companion papers to establish the: (3) existence of, uniqueness of and convergence to martingale problem solutions, (4) classical Fujisaki-Kallianpur-Kunita and Duncan-Mortensen-Zakai filtering equations and stationary filters, (5) finite-dimensional convergence to stationary signal-filter pairs, (6) invariant measures of Markov processes, and (7) Ray-Knight theory all in general settings.
