This article is cited in 2 papers

Short Communications

Multimodal convolutions of unimodal infinitely divisible distributions

K. Sato

Department of Mathematics, Nagoya University, Nagoya, Japan

Abstract: 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 $0<t<1$, is unimodal for $t=1$ and is $n$-modal for $t=2$.

Keywords: infinitely divisible distributions, unimodal distribution, $n$-modal distribution, Lévy process, convolution.

Received: 02.09.1993

Language: English

 English version: Theory of Probability and its Applications, 1994, 39:2, 336–347

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