Abelian and Tauberian theorems for the Laplace transform of functions in several variables

DOI10.1016/0047-259X(89)90041-9zbMath0684.44002MaRDI QIDQ1825398

Yanyan Li

Publication date: 1989

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

Laplace transformsasymptotic behaviourTauberian theoremsAbelian theoremsasymptotics of convolutionsbivariate sequencesbivariate power seriesbivariate renewal functionfunctions of weak regular variation

Mathematics Subject Classification ID

Laplace transform (44A10) Integral transforms of special functions (44A20) Renewal theory (60K05) Multiple integral transforms (44A30)

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Three approaches in the study of recurrent Markovian and semi-Markovian processes ⋮ Multivariate weighted renewal functions ⋮ Subexponential distribution functions in \(R^{d}\) ⋮ Moments of a non‐homogenous bi‐variate fragmentation process using integral equations tools ⋮ The distribution of unobserved heterogeneity in competing risks models ⋮ Approximations in bivariate renewal theory ⋮ Local asymptotics for the area of random walk excursions ⋮ Multivariate subexponential distributions and random sums of random vectors

Cites Work

• Integrals and derivatives of regularly varying functions in \(R^ n\) and domains of attraction of stable distributions. II
• Domains of attraction and regular variation in \({\mathbb{R}}^ d\)
• Derivatives of regularly varying functions in \(R^d\) and domains of attraction of stable distributions
• Renewal theory in two dimensions: asymptotic results
• Renewal theory in two dimensions: Basic results
• Renewal Theory in the Plane
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