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A Second‐Order Theorem for Laplace Transforms
Author(s) -
Embrechts Paul
Publication year - 1978
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-17.1.102
Subject(s) - laplace transform , converse , mathematics , order (exchange) , class (philosophy) , constant (computer programming) , pure mathematics , mathematical analysis , function (biology) , combinatorics , geometry , computer science , finance , economics , artificial intelligence , evolutionary biology , biology , programming language
We prove that second order information of the forml i m t → ∞B ( t ) − b ( 1 / t )t − 1∫ 0 t s d B ( s )= γ (Euler's constant), where b is the Laplace transform of a positive, non‐decreasing function B on R + , necessarily implies that B belongs to a specified sub‐class of the class of slowly varying functions. This proves a converse to a theorem of de Haan.