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, vol.353, pp.179-190, 2019 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 353
  • Publication Date: 2019
  • Doi Number: 10.1016/j.cam.2018.12.014
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.179-190
  • Keywords: Geometric process, Geometric function, Integral equation, Laplace transform, Second moment function, Tauberian theorem, QUASI-RENEWAL PROCESS
  • Ankara University Affiliated: Yes

Abstract

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.