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• W2517797271 abstract "Under some suitable conditions, we show that, for a distribution $F$ supported on $[0,infty)$ and a nonnegative integer-valued random variable $tau$ with masses $p_k=P(tau=k),kge0$, if their random convolution $F^{*tau}=sum_{k=0}^infty p_kF^{*k}$ belongs to exponential and generalised subexponential distribution class $mathcal{L}(gamma)capmathcal{OS}$ for some $gammage0$, then there is an integer $n_0ge1$ such that $F^{*n}$ also belongs to the class for all $nge n_0$. Further, if $Finmathcal{OS}$, then $Finmathcal{L}(gamma)$. And we do some in-depth discussion about the above conditions, and provide some types of distributions satisfying them. In addition, we also give three local versions of the above result by the Esscher transform of distributions. Finally, the main and ultimate goal of the paper is introduced that we apply the results to the theory of infinitely divisible distribution with some technical details." @default.
• W2517797271 created "2016-09-16" @default.
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• W2517797271 date "2016-09-04" @default.
• W2517797271 modified "2023-09-23" @default.
• W2517797271 title "Some positive conclusions on the closedness under the random convolution roots for certain distribution classes" @default.
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