Limit Theorems for Stochastic Processes
Limit Theorems for Stochastic Processes
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DOI：
10.1137/1101022
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发表时间：
1956
影响因子：
0.6
通讯作者：
A. Skorokhod
中科院分区：
文献类型：
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作者：
A. Skorokhod
让我们考虑一个过程序列$\xi _n（t）$，使得$\xi _n（t_1），\xi _n（t_2），\cdots，\xi _n（t_k）$的多元分布对所有k和$t_1，t_2，\cdots，\xi_0（t_1），\xi_0（t_2），\cdots，\xi_0（t_k）$趋于$\xi_0（t_1），\xi_0（t_2），\cdots，\xi_0（t_k）$的多元分布，t_k $.设f是使$f（\xi _n（t））$以概率1确定，后者是随机变量（即具有概率分布的那些）。本文包含几个充分条件，其中f的分布（\xi _n（t））$趋向于$f的分布（\xi _0（t））$ as $n \to \infty $.设K是不具有高于简单跳跃的间断的所有函数的空间，假设$\xi _n（t）$在K中的概率为1。给出了在这些拓扑中连续的泛函f的分布趋于f（\xi _n（t））分布的充要条件，并给出了相应的结果.
Let us consider a sequence of processes $\xi _n (t)$ such that the multivariate distribution of $\xi _n (t_1 ),\xi _n (t_2 ), \cdots ,\xi _n (t_k )$ tends to the multivariate distribution of $\xi _0 (t_1 ),\xi _0 (t_2 ), \cdots ,\xi _0 (t_k )$ for all k and $t_1 ,t_2 , \cdots ,t_k $.Let f be the functional for which $f(\xi _n (t))$ are determined with a probability of 1, the latter being random variables (i.e, those that have probability distributions).This paper contains several sufficient conditions, for which the distributions of $f(\xi _n (t))$ tend to the distribution of $f(\xi _0 (t))$ as $n \to \infty $.Let K be the space of all functions not having discontinuities higher than simple jumps, and let us assume that $\xi _n (t)$ with a probability of 1 is in K.Several topologies in K are defined. The necessary and sufficient conditions are found for all functionals f that are continuous in these topologies for which the distribution of $f(\xi _n (t))$ tends to the distribution of $f(\xi _0 (t))$.The r...