On a denseness result for quasi-infinitely divisible distributions
Statistics & Probability Letters, 2021, vol. 176, issue C
A probability distribution μ on Rd is quasi-infinitely divisible if its characteristic function has the representation μ̂=μ1̂∕μ2̂ with infinitely divisible distributions μ1 and μ2. In Lindner et al. (2018, Thm. 4.1) it was shown that the class of quasi-infinitely divisible distributions on R is dense in the class of distributions on R with respect to weak convergence. In this paper, we show that the class of quasi-infinitely divisible distributions on Rd is not dense in the class of distributions on Rd with respect to weak convergence if d≥2.
Keywords: Denseness; Quasi-infinitely divisibility; Zeros of characteristic functions (search for similar items in EconPapers)
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