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Esscher transform : ウィキペディア英語版
Esscher transform
In actuarial science, the Esscher transform is a transform that takes a probability density ''f''(''x'') and transforms it to a new probability density ''f''(''x''; ''h'') with a parameter ''h''. It was introduced by F. Esscher in 1932 .
==Definition==

Let ''f''(''x'') be a probability density. Its Esscher transform is defined as
:f(x;h)=\frac f(x) dx}.\,
More generally, if ''μ'' is a probability measure, the Esscher transform of ''μ'' is a new probability measure ''Eh''(''μ'') which has density
:\frac^\infty e^ d\mu(x)}
with respect to ''μ''.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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