Exponential Expansions for Perturbed Discrete Time Renewal Equations
2013 (English)In: Applied Reliability Engineering and Risk Analysis: Probabilistic Models and Statistical Inference / [ed] Ilia B. Frenkel, Alex Karagrigoriou, Anatoly Lisnianski, Andre Kleyner, Chichester: John Wiley & Sons, 2013, 349-362 p.Chapter in book (Refereed)
This chapter presents results about the asymptotic behavior of the solution x(φ)(n) of a perturbed discrete time renewal equation as φ--> 0 and n-->? simultaneously. It consider two cases of so-called quasi-stationary and pseudo-stationary asymptotics, where the limiting distribution f (0)(k) may be, respectively, improper or proper. The author improves the asymptotic relation to the much more advanced form of an exponential asymptotic expansion. The chapter illustrates theoretical results by examples related to queuing systems and risk processes. It briefly shows the way of getting the renewal equation. It repeats the method of finding a similar continuous time renewal equation for ruin probabilities, given, for example in Feller (1966) and Grandell (1991).
Place, publisher, year, edition, pages
Chichester: John Wiley & Sons, 2013. 349-362 p.
perturbed discrete time renewal, pseudo-stationary asymptotics, quasi-stationary asymptotics, queuing systems, risk processes
Probability Theory and Statistics
Research subject Mathematical Statistics
IdentifiersURN: urn:nbn:se:su:diva-95461DOI: 10.1002/9781118701881.ch23ISBN: 9781118539422ISBN: 9781118701881OAI: oai:DiVA.org:su-95461DiVA: diva2:660252