An inequality for multiple convolutions with respect to Dirichlet probability measure

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• 作者：Arcadii Z. Grinshpan ^{agrinshp@usf.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：26D15 ; 33B15 ; 33E15
• 刊名：Advances in Applied Mathematics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：82
• 期：Complete
• 页码：102-119
• 全文大小：396 K

文摘

A sharp multiple convolution inequality with respect to Dirichlet probability measure on the standard simplex is presented. Its discrete version in terms of the negative binomial coefficients is proved as well. The new bounds for the Dirichlet distribution and iterated convolutions are obtained as the consequences of the main result. Also some binomial, exponential, and generalized hypergeometric applications are discussed.