An asymptotic solution of the integral equation for the second moment function in geometric processes

PEKALP M. H., AYDOĞDU H.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.353, ss.179-190, 2019 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 353
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1016/j.cam.2018.12.014
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.179-190
  • Anahtar Kelimeler: Geometric process, Geometric function, Integral equation, Laplace transform, Second moment function, Tauberian theorem, QUASI-RENEWAL PROCESS
  • Ankara Üniversitesi Adresli: Evet

Özet

In this study, we derive an asymptotic solution of the integral equation satisfied by the second moment function M-2 (t, a). We first find the Laplace transform (M-2)(L) (s, a) and then obtain M-2 (t, a) asymptotically by inversion. Further, we have derived the asymptotic expressions of M-2 (t, a) for some special lifetime distributions such as exponential, gamma, Weibull, lognormal and truncated normal. Finally, the asymptotic solution is compared with the numerical solution to evaluate its performance. (C) 2018 Elsevier B.V. All rights reserved.