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Truncated random variables with application to random surfaces
Author(s) -
Phillips M. J.,
Roach G. F.
Publication year - 1984
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670060117
Subject(s) - mathematics , random variable , gaussian , connection (principal bundle) , statistical physics , surface (topology) , sum of normally distributed random variables , multivariate random variable , random element , random field , statistics , geometry , physics , quantum mechanics
There has been considerable interest in obtaining discrete results for random surfaces. Standard results have been published in journals of physics or engineering which have emphasised the applications. This paper gives a detailed background of the mathematical methods needed so that the central connection, namely truncated random variables, between these standard results can be understood. Distributions of discrete peak measures are obtained from the distributions of discrete profile measures of a random Gaussian surface by applying results for the distributions of truncated random variables. This enable the moments to be obtained from known results for the truncated distributions.