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The Maximal Strichartz Family of Gaussian Distributions: Fisher Information, Index of Dispersion, and Stochastic Ordering
Author
Source
International Journal of Differential Equations
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-09-29
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
We define and study several properties of what we call Maximal Strichartz Family of Gaussian Distributions.
This is a subfamily of the family of Gaussian Distributions that arises naturally in the context of the Linear Schrödinger Equation and Harmonic Analysis, as the set of maximizers of certain norms introduced by Strichartz.
From a statistical perspective, this family carries with itself some extrastructure with respect to the general family of Gaussian Distributions.
In this paper, we analyse this extrastructure in several ways.
We first compute the Fisher Information Matrix of the family, then introduce some measures of statistical dispersion, and, finally, introduce a Partial Stochastic Order on the family.
Moreover, we indicate how these tools can be used to distinguish between distributions which belong to the family and distributions which do not.
We show also that all our results are in accordance with the dispersive PDE nature of the family.
American Psychological Association (APA)
Selvitella, Alessandro. 2016. The Maximal Strichartz Family of Gaussian Distributions: Fisher Information, Index of Dispersion, and Stochastic Ordering. International Journal of Differential Equations،Vol. 2016, no. 2016, pp.1-17.
https://search.emarefa.net/detail/BIM-1105685
Modern Language Association (MLA)
Selvitella, Alessandro. The Maximal Strichartz Family of Gaussian Distributions: Fisher Information, Index of Dispersion, and Stochastic Ordering. International Journal of Differential Equations No. 2016 (2016), pp.1-17.
https://search.emarefa.net/detail/BIM-1105685
American Medical Association (AMA)
Selvitella, Alessandro. The Maximal Strichartz Family of Gaussian Distributions: Fisher Information, Index of Dispersion, and Stochastic Ordering. International Journal of Differential Equations. 2016. Vol. 2016, no. 2016, pp.1-17.
https://search.emarefa.net/detail/BIM-1105685
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1105685