Dominated variation and related concepts and Tauberian theorems for Laplace transforms

DOI10.1016/0022-247X(85)90030-7zbMath0581.44003MaRDI QIDQ1068314

Laurens De Haan, Ulrich Stadtmüller

Publication date: 1985

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Laplace-Stieltjes transformTauberian theoremsAbelian theorems

Mathematics Subject Classification ID

Laplace transform (44A10) Tauberian theorems (40E05)

Related Items

Brownian motion on the Sierpinski gasket, Asymptotic properties of absolutely continuous functions and strong laws of large numbers for renewal processes, Sample function behavior of increasing processes of class \(L\), Asymptotically balanced functions and the asymptotic behaviour of the complementary function and the Laplace transform, The weak asymptotic equivalence and the generalized inverse, Asymptotics for the joint tail probability of bidimensional randomly weighted sums with applications to insurance, Symmetric Birkhoff sums in infinite ergodic theory, Optimal rates of decay in the Katznelson-Tzafriri theorem for operators on Hilbert spaces, Tauberian theorems for \(J_ p\)-summability, On-diagonal oscillation of the heat kernels on post-critically finite self-similar fractals, On lower tail probabilities of positive random sums, An Abel-Tauber theorem for partitions. II, Second-order regular variation inherited from Laplace–Stieltjes transforms, The dimension of the boundary of super-Brownian motion, Passage times of random walks and Lévy processes across power law boundaries

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotically balanced functions and stochastic compactness of sample extremes
• A weak invariance principle with applications to domains of attraction
• Stochastic compactness of sample extremes
• Neuer Beweis und Verallgemeinerung einiger Tauberian-Sätze
• Über einen Satz von Vijayaraghavan
• Extensions of Regular Variation, II: Rerpresentations and Indices
• Regularly varying functions in the theory of simple branching processes
• An Abel-Tauber Theorem for Laplace Transforms
• A Second-Order Theorem for Laplace Transforms
• On Tauberian Theorems
• Tauberian Theorems and Slowly Varying Functions
• Regularly increasing functions in connection with the theory of $L^{*φ}$-spaces