On a denseness result for quasi-infinitely divisible distributions

9 Mar 2021  ·  Merve Kutlu ·

A probability distribution $\mu$ on $\mathbb{R}^d$ is quasi-infinitely divisible if its characteristic function has the representation $\widehat{\mu} = \widehat{\mu_1}/\widehat{\mu_2}$ with infinitely divisible distributions $\mu_1$ and $\mu_2$. In \cite[Thm... 4.1]{lindner2018} it was shown that the class of quasi-infinitely divisible distributions on $\mathbb{R}$ is dense in the class of distributions on $\mathbb{R}$ with respect to weak convergence. In this paper, we show that the class of quasi-infinitely divisible distributions on $\mathbb{R}^d$ is not dense in the class of distributions on $\mathbb{R}^d$ with respect to weak convergence if $d \geq 2$. read more

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Probability 60E07, 60E10 (Primary) 60E05 (Secondary)