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Yuji Kasahara - One of the best experts on this subject based on the ideXlab platform.
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remarks on tauberian theorem of exponential type and fenchel legendre transform
Osaka Journal of Mathematics, 2002Co-Authors: Yuji Kasahara, Nobuko KosugiAbstract:Let ( ), ≥ 0 be a nondecreasing Right-Continuous Function such that (0) = 0. The asymptotics of and its Laplace-Stieltjes transform ω( ) = ∫∞ 0 − ( ) are closely linked and results in which we pass from ( ) to ω( ) are called Abelian theorems and ones in converse direction are called Tauberian, and they play a very important role in probability theory. A most well-known result on this subject is Karamata’s theorem (cf. Chapter 1 of [1]). Also the cases when ω( ) and ( ) vary exponentially are treated by many authors (e.g. [2], [3], [4], [8], [9]. See also Chapter 4 of [1]). Among them [2] studied the relationship between the limit of (1/λ) log (1/φ(λ)) as λ → ∞ and that of the Laplace-Stieltjes transform modified as
Nobuko Kosugi - One of the best experts on this subject based on the ideXlab platform.
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remarks on tauberian theorem of exponential type and fenchel legendre transform
Osaka Journal of Mathematics, 2002Co-Authors: Yuji Kasahara, Nobuko KosugiAbstract:Let ( ), ≥ 0 be a nondecreasing Right-Continuous Function such that (0) = 0. The asymptotics of and its Laplace-Stieltjes transform ω( ) = ∫∞ 0 − ( ) are closely linked and results in which we pass from ( ) to ω( ) are called Abelian theorems and ones in converse direction are called Tauberian, and they play a very important role in probability theory. A most well-known result on this subject is Karamata’s theorem (cf. Chapter 1 of [1]). Also the cases when ω( ) and ( ) vary exponentially are treated by many authors (e.g. [2], [3], [4], [8], [9]. See also Chapter 4 of [1]). Among them [2] studied the relationship between the limit of (1/λ) log (1/φ(λ)) as λ → ∞ and that of the Laplace-Stieltjes transform modified as
