论文标题
关于准无限划分定律的弱收敛性
On weak convergence of quasi-infinitely divisible laws
论文作者
论文摘要
我们研究了一类新的所谓准准法律法律，这是通过lévy-khinchine-khinchine类型表示的无限分裂定律的广泛自然扩展。我们对此类融合薄弱的标准感兴趣。在相当自然的假设下，我们指出的断言将准绝对可划分的分布函数与lévy-khinchine频谱函数的一种特殊类型的收敛性联系在一起。后一种收敛不等于弱收敛性。因此，我们补充了Lindner，Pan和Sato（2018）在该领域的已知结果。
We study a new class of so-called quasi-infinitely divisible laws, which is a wide natural extension of the well known class of infinitely divisible laws through the Lévy--Khinchine type representations. We are interested in criteria of weak convergence within this class. Under rather natural assumptions, we state assertions, which connect a weak convergence of quasi-infinitely divisible distribution functions with one special type of convergence of their Lévy--Khinchine spectral functions. The latter convergence is not equivalent to the weak convergence. So we complement known results by Lindner, Pan, and Sato (2018) in this field.
