Extension Of Positive Definite Distributions And Maximum Entropy
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Extension of Positive-Definite Distributions and Maximum Entropy
Author: Jean-Pierre Gabardo
language: en
Publisher: American Mathematical Soc.
Release Date: 1993
In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.
Extension of Positive-Definite Distributions and Maximum Entropy.
Author: Jean-Pierre Gabardo
language: en
Publisher: American Mathematical Society(RI)
Release Date: 2014-08-31
In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.
Markov Fields over Countable Partially Ordered Sets: Extrema and Splitting
Author: I. V. Evstigneev
language: en
Publisher: American Mathematical Soc.
Release Date: 1994
Various notions of the Markov property relative to a partial ordering have been proposed by both physicists and mathematicians. This work develops techniques for stying Markov fields on partially ordered sets. We introduce random transformations of the index set which preserves the Markov property of the field. These transformations yield new classes of Markov fields starting from relatively simple ones. Examples include a model for crack formation and a model for the distribution of fibres in a composite material.