论文标题
随机过程的密度特性
A density property for stochastic processes
论文作者
论文摘要
考虑一类概率分布，在$ \ mathbb {r}^{d} $相对于弱收敛的所有概率分布的空间中，对于\ mathbb {n} $而言。然后，我们构建了各种显式的连续（Cádlág）过程，这些过程在所有连续（Cádlág）过程的空间中相对于分布的收敛。这是由于最近的结果是，当$ d = 1 $时，准绝对可划分（QID）分布是密集的。如果将此结果扩展到\ Mathbb {n} $中的任何$ d \，那么我们的结果将暗示QID过程在连续和Cádlág流程的两个空间中均密集。
Consider a class of probability distributions which is dense in the space of all probability distributions on $\mathbb{R}^{d}$ with respect to weak convergence, for every $d\in\mathbb{N}$. Then, we construct various explicit classes of continuous (cádlág) processes which are dense in the space of all continuous (cádlág) processes with respect to convergence in distribution. This is motivated by the recent result that quasi-infinitely divisible (QID) distributions are dense when $d=1$. If this result is extended to any $d\in\mathbb{N}$, then our result will imply that QID processes are dense in both spaces of continuous and cádlág processes.
