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

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  • Omey, E.
  • Willekens, E.

Abstract

Using two kinds of multivariate regular variation we prove several Abel-Tauber theorems for the Laplace transform of functions in several variables. We generalize some power series results of Alpar and apply our results in multivariate renewal theory.

Suggested Citation

  • Omey, E. & Willekens, E., 1989. "Abelian and Tauberian theorems for the Laplace transform of functions in several variables," Journal of Multivariate Analysis, Elsevier, vol. 30(2), pages 292-306, August.
    • Handle: RePEc:eee:jmvana:v:30:y:1989:i:2:p:292-306
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    Cited by:

    1. Boyan Dimitrov & Vladimir Rykov & Tatiana Milovanova, 2020. "Renewal Redundant Systems Under the Marshall–Olkin Failure Model. A Probability Analysis," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    2. Mallor, F. & Omey, E. & Santos, J., 2007. "Multivariate weighted renewal functions," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 30-39, January.
    3. Yang Lu, 2020. "The distribution of unobserved heterogeneity in competing risks models," Statistical Papers, Springer, vol. 61(2), pages 681-696, April.

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