A density property for stochastic processes
A density property for stochastic processes
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随机过程的密度属性
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发表时间：
2020
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通讯作者：
Riccardo Passeggeri
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作者：
Riccardo Passeggeri
考虑一类概率分布，它在$mathbb{R}^{d}$上的所有概率分布的空间中就弱收敛而言是稠密的，对每一个$dinmathbb{N}$。然后，我们构造了各种明确的类的连续（cadlag）的过程是密集的空间中的所有连续（cadlag）的过程在分布收敛。这是由最近的结果，准无限可分（QID）的分布是密集的，当$d=1$。如果把这个结果推广到任意的dinmathbb{N}，那么我们的结果将意味着QID过程在连续和cadlag过程空间中都是稠密的.
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 $dinmathbb{N}$. Then, we construct various explicit classes of continuous (cadlag) processes which are dense in the space of all continuous (cadlag) 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 $dinmathbb{N}$, then our result will imply that QID processes are dense in both spaces of continuous and cadlag processes.