Geodesic
Multimodal convolutions of unimodal infinitely divisible distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 2, pp. 403-415

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For any positive integer $n$ an infinitely divisible distribution on $(0,\infty)$ such that its convolution with itself is $n$-modal is constructed. Moreover, we constructed the Lévy process $X_t$, $t\ge 0$, with the following properties: the distribution $X_t$ is not unimodal for $0$, is unimodal for $t=1$ and is $n$-modal for $t=2$.
Keywords: infinitely divisible distributions, unimodal distribution, Lévy process
Mots-clés : $n$-modal distribution, convolution. 
@article{TVP_1994_39_2_a9,
     author = {K. Sato},
     title = {Multimodal convolutions of unimodal infinitely divisible distributions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {403--415},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1994_39_2_a9/}
}
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K. Sato. Multimodal convolutions of unimodal infinitely divisible distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 2, pp. 403-415. http://geodesic.mathdoc.fr/item/TVP_1994_39_2_a9/