Quasi-Stationary Distributions for Perturbed Discrete Time Regenerative Processes
2014 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 89, 153-168 p.Article in journal (Refereed) Published
Non-linearly perturbed discrete time regenerative processes with regenerative stopping times are considered. We define the quasi-stationary distributions for such processes and present conditions for their convergence. Under some additional assumptions, the quasi-stationary distributions can be expanded in asymptotic power series with respect to the perturbation parameter. We give an explicit recurrence algorithm for calculating the coefficients in these asymptotic expansions. Applications to perturbed alternating regenerative processes with absorption and perturbed risk processes are presented.
Place, publisher, year, edition, pages
2014. Vol. 89, 153-168 p.
Regenerative process, Renewal equation, Non-linear perturbation, Quasi-stationary distribution, Asymptotic expansion, Risk process
Probability Theory and Statistics
Research subject Mathematical Statistics
IdentifiersURN: urn:nbn:se:su:diva-95468OAI: oai:DiVA.org:su-95468DiVA: diva2:660265