From doubly stochastic representations of K distributions to random walks and back again: an optics tale

A random walk model with a negative binomially fluctuating number of steps is considered in the case where the mean of the number fluctuations,, is finite. The asymptotic behaviour of the resultant statistics in the large limit is derived and shown to give the K distribution. The equivalence of this...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 42; no. 22; pp. 225007 - 225007 (13)
Main Author French, O E
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 05.06.2009
IOP
Subjects
Exact sciences and technology
Physics
Fluctuations
Random walk model
Equivalence
Random walk
Asymptotic behavior
Probability density function
Random distribution
Bunching
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Summary:A random walk model with a negative binomially fluctuating number of steps is considered in the case where the mean of the number fluctuations,, is finite. The asymptotic behaviour of the resultant statistics in the large limit is derived and shown to give the K distribution. The equivalence of this model to the hitherto unrelated doubly stochastic representation of the K distribution is also demonstrated. The convergence to the K distribution of the probability density function generated by a random walk with a finite mean number of steps is examined along with the moments, and the non-Gaussian statistics are shown to be a direct result of discreteness and bunching effects.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/42/22/225007