Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

Nonlinearly perturbed renewal equations: The nonpolynomial case


Author: Ying Ni
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 84 (2011).
Journal: Theor. Probability and Math. Statist. 84 (2012), 117-129
MSC (2010): Primary 60K05, 34E10; Secondary 60K25
Published electronically: July 31, 2012
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Models of nonlinearly perturbed renewal equations with nonpolynomial perturbations are studied. Exponential asymptotic expansions are given for the solutions to the perturbed renewal equations under consideration. An application to perturbed M/G/1/ queues is presented.


References [Enhancements On Off] (What's this?)

  • 1. Søren Asmussen, Ruin probabilities, Advanced Series on Statistical Science & Applied Probability, vol. 2, World Scientific Publishing Co. Inc., River Edge, NJ, 2000. MR 1794582 (2001m:62119)
  • 2. William Feller, An introduction to probability theory and its applications. Vol. II., Second edition, John Wiley & Sons Inc., New York, 1971. MR 0270403 (42 #5292)
  • 3. Mats Gyllenberg and Dmitrii S. Silvestrov, Quasi-stationary phenomena in nonlinearly perturbed stochastic systems, de Gruyter Expositions in Mathematics, vol. 44, Walter de Gruyter GmbH & Co. KG, Berlin, 2008. MR 2456816 (2009k:60005)
  • 4. Y. Ni, D. Silvestrov, and A. Malyarenko, Exponential asymptotics for nonlinearly perturbed renewal equation with non-polynomial perturbations, J. Numer. Appl. Math. 1(96) (2008), 173-197.
  • 5. Y. Ni, Analytical and numerical studies of perturbed renewal equations with multivariate non-polynomial perturbations, Journal of Applied Quantitative Methods 5(3) (2010a), 498-515.
  • 6. Y. Ni, Perturbed Renewal Equations with Non-polynomial Perturbations, Licentiate Thesis, Mälardalen University, 2010b.
  • 7. D. S. Sīl′vestrov, A generalization of the renewal theorem, Dokl. Akad. Nauk Ukrain. SSR Ser. A 11 (1976), 978–982, 1052 (Russian, with English summary). MR 0483057 (58 #3086)
  • 8. D. S. Sīl′vestrov, The renewal theorem in the scheme of series. I, Teor. Verojatnost. i Mat. Statist. 18 (1978), 144–161, 183 (Russian, with English summary). MR 0488350 (58 #7899)
  • 9. D. S. Sīl′vestrov, The renewal theorem in the scheme of series. II, Teor. Veroyatnost. i Mat. Statist. 20 (1979), 97–116, 158 (Russian, with English summary). MR 529265 (80g:60092)
  • 10. D. S. Silvestrov, Exponential asymptotics for a perturbed renewal equation, Teor. Ĭmovīr. Mat. Stat. 52 (1995), 143–153 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 52 (1996), 153–162. MR 1445549 (97m:60127)

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 60K05, 34E10, 60K25

Retrieve articles in all journals with MSC (2010): 60K05, 34E10, 60K25


Additional Information

Ying Ni
Affiliation: Division of Applied Mathematics, School of Education, Culture, and Communication, Mälardalen University, Västerås 721 23, Sweden
Email: ying.ni@mdh.se

DOI: http://dx.doi.org/10.1090/S0094-9000-2012-00865-X
PII: S 0094-9000(2012)00865-X
Keywords: Perturbed renewal equation, nonpolynomial perturbation
Received by editor(s): October 30, 2010
Published electronically: July 31, 2012
Article copyright: © Copyright 2012 American Mathematical Society