Limitation of Log-Normal Theory of Turbulence

概要

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The probability distribution of the sum of n independent random variables withfinite mean and finite variance does not generally approach the normal distributionwith variance proportional to n, contrary to the log-normal theory of turbulence inwhich the central limit theorem is applied in an easy manner. Although the expecta-lions of all the moments of the sum agree with those of the limiting normal distribu-tion in the leading order for n >>l, the moments of the exponential of the sum do not.Thus the log-normal theory is not so robust as expected from the generality of the cen-tral limit theorem.
社団法人日本物理学会の論文
1991-02-15