Hamburger moment problem and Maximum Entropy: On the existence conditions

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• 作者：A. Tagliani ^{aldo.tagliani@unitn.it" class="auth_mail}
• 关键词：Reduced Hamburger moment problem ; Hankel determinant ; Maximum Entropy ; Moment ; Moment space
• 刊名：Applied Mathematics and Computation
• 出版年：15 March, 2014
• 年：2014
• 卷：231
• 期：Complete
• 页码：111-116
• 全文大小：465 K

文摘

The existence of Maximum Entropy solution for the reduced Hamburger moment problem is reconsidered. Existence conditions, previously appeared in literature, are revisited allowing an easy way to identifying the existence of Maximum Entropy solution. The obtained results suggest that, except for special sequences of moments unknown a priori, the Maximum Entropy solution for the non symmetric reduced Hamburger moment problem exists. For practical purposes, the replacing of the support with a large enough finite interval finds a theoretical warranty. The symmetric case may be formulated as follows: once assigned the first moments, if MaxEnt density does not exist (conclusion drawn uniquely from numerical evidence), MaxEnt density with the first moments exists. In such a case, even if the first moments are known, we have to settle for a density which carries less information. Theoretical results are illustrated through some numerical examples.